Aea?aeaaiee oi?aa?neoao «Euea?anueea iie?oaoi?ea»

*aaai Aiae??e Aaneeueiae/

OAeE 681.142.2: 621.3.013

IaOAIAOE*IA IIAeAETHAAIIss AeAIOI*EIAEO T-IA?iIAeE*Ieo E?AEIAEO
caaea* aeaeo?iaeeiaiIee IaOAIAOE*IA IIAeAETHAAIIss
AeAIOI*EIAEO T-IA?iIAeE*Ieo E?AEIAEO caaea* aeaeo?iaeeiaiIee

Niaoeiaeueiinoue

01.05.02 — Iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe

Euea?a — 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia ia eaoaae?? aeaeo?iiinoa/aiiy oa aeaeo?ioaoi?ee
Eooeueeiai aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani? Eaeaithe
Iao?i I?aaiiae/, Aea?-aeaaiee oi?aa?neoao “Euea?anueea iie?-oaoi?ea”,
caa?aeoaa/ eaoaae?e ia/en-ethaaeueii? iaoaiaoeee oa i?ia?aio-aaiiy

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,i?ioani?
Neiiueianueeee ?iiai Aieiaee-ie?iae/, Aea?aeaaiee oi?aa?neoao
“Euea?anueea iie?oaoi?ea”, i?ioani? ea-oaae?e i?eeeaaeii? iaoaiaoeee;

aeieoi? oaoi?/ieo iaoe, eao?aao aea?aea-aii? i?ai?? a aaeoc? iaoee e
oaoi?ee, i?ioani? Naia?ae Ieoaeei Ieoaeei-ae/, Euea?anueeee aea?aeaaiee
aa?a?iee oi?aa?neoao, caa?aeoaa/ eaoaae?e o?ce-ee.

I?ia?aeia onoaiiaa — Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea,
eaoaae?a iiaeaethaaiiy neeaaeieo nenoai.

Caoeno a?aeaoaeaoueny “16” ea?oiy 1999 ?. i 14 aiae. 00 oa.
iacan?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 35.052.05 i?e Aea?aeaaiiio
oi?aa?neoao? “Euea?anueea iie?oaoi?ea” (290646, i. Euea?a, aoe. N.
Aaiaea?e, 12).

C aeena?oaoe??th iiaeia iciaeiieoeny a iaoeiai-oaoi?/i?e a?ae?ioaoe?
Aea?aeaaiiai oi?aa?neoaoo “Euea?anueea iie?oaoi?ea” (290646, i. Euea?a,
aoe. I?ioani?nueea, 1).

Aaoi?aoa?ao ?ic?neaiee “ 12 ” aa?aciy 1999 ?.

A/aiee nae?aoa? niaoe?ae?ciaaii? a/aii?

?aaee, eaiaeeaeao oaoi?/ieo iaoe, aeioeaio N. I. Oea/aiei

1

Caaaeueia oa?aeoa?enoeea ?iaioeCaaaeueia oa?aeoa?enoeea ?iaioe

Aeooaeuei?noue i?iaeaie. Caaea/a aiae?co aoaeue-yei? o?ce/ii? nenoaie
neeaaea?oueny c /ioe?ueio aoai?a: ?ic?aooieo ia?ao?aeiiai e onoaeaiiai
i?i-oean?a, aecia/aiiy noaoe/ii? no?eeino? ?, iae?iaoeue, ?ic?aooieo
ia?aiao-?e/ii? /ooeeaino?. Aei iaaeaaiueiai /ano ?aae?caoe?y eiaeiiai c
oeeo aoai?a cae?enithaaeany ??ciei iaoaiaoe/iei aia?aoii. ?ic??ciai?
aeai?eoie aeiaaaee ?ic??ciaieo ciaiue c iaoaiaoeee. Aiie ?aae?coaaeeny,
ca aeiyoeii ia?oiai aoaio, a iica/ania?e iaeano?, a, a?aeoae, aoee
iicaaaeai? iiaeeeaino? eiio?ieth oi/iino?, ai ia?aaeaa/aee aieueiaa
ao?o/aiiy a ia/enethaaeueiee i?ioean. Oaia? aeii?iothoue ia/enethaaeuei?
iaoiaee. Ia ?o i?aenoaa? caaaeueia oai??y iae?i?eieo aeeoa?aioe?aeueieo
??aiyiue oiiaeeeaeea ?ica’ycaoe caaea/o aiae?co aoe?eiio ia iniia?
?aeaioe/iiai iaoaiaoe/iiai aia?aoa a /ania?e iaeano?.

O aeai?e ?iaio? i?iaeaia caoaeo?oueny aei aiae?co onoaeaieo i?ioean?a o
i?inoi?iaeo caaea/ao aeaeo?iaeeiai?ee. ?acoeueoaoe aeeiiaieo
aeine?aeaeaiue iiaeia canoiniaoaaoe aei aoaeue-yeeo o?ce/ieo i?ioean?a,
ui iienothoueny aeeoa?aioe?aeueieie ??aiyiiyie ?c cae/aeieie e
/anoeiieie iio?aeieie. Iia?oth/e iae?i?eieie aeeoa?aioe?aeueieie
??aiyiiyie a /ania?e iaeano?, ie aaoiiaoe/ii ioiieth?ii aoai aiae?co
ia?ao?aeieo i?ioean?a ye oaeee, ui ? ?acoeueoaoii ?ioaa?oaaiiy
aeeoa?aioe?aeueieo ??aiyiue ca /anii.

Aiae?c ia?ao?aeieo i?ioean?a iieyaa? a ?ica’ycaii? caaea/? Eio? aeey
iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue. Iaea?oa?oee iaoiae iaea?aeaiiy
onoaeaiiai i?ioeano — ?ioaa?oaaiiy aeeoa?aioe?aeueieo ??aiyiue noaio aae
aei onoaeaiiy, ui iaaei?aaaeaii ?c-ca iaiii??iiai iaeiie/aiiy iioeaie
?ioaa?oaaiiy ? cao?ao iaoeiiiai /ano. Oiio aeioe?eueii ei?enooaaoenue
iaoiaeaie i?enei?aiiai iiooeo aeiooaieo ia??iaee/ieo ?aaeei?a. Iaoiaee
iica/aniai? iaeano? aeathoue ciiao aecia/eoe eeoa i?inoi?iaee ?iciiae?e
ooieoe?? o iaaiee iiiaio /ano, a aeey io?eiaiiy ?? i?inoi?iai-/aniaiai
?iciiae?eo iaiao?aeia aaaaoi?aciaa ?ica’ycaiiy caaea/? aeey ?yaeo
aeene?aoieo cia/aiue /ano t. Iaoiaee /aniai? iaeano? aeathoue
iiaeeea?noue iaea?aeaoe i?inoi?iai-/aniaee ?iciiae?e ooieoe??. Aiie
iiae?eythoueny ia iaoiaee, ui a?oioothoueny ia iiaoaeia? iiaeaeae
/ooeeaino? aei ii/aoeiaeo oiia, aeno?aiieyoe?ei? oa a?aae??ioi?.
?ic?aooiie onoaeaiiai i?ioeano a oeeo iaoiaeao caiaeeoueny aei
?ioaa?oaaiiy ??aiyiue noaio a?ae aeayeeo ii/aoeiaeo oiia, ui
aeeeth/athoue ia?ao?aeio ?aaeoe?th. I?iaeaia iieyaa? naia o aecia/aii?
oaeeo ii/aoeiaeo oiia. Aeey neeaaeieo aeai- ? o?eaei??ieo i?inoi?iaeo
caaea/ aeaeo?iaeeiai?ee oi?aa?naeuei? iaoiaee i?enei?aiiai iiooeo
onoaeaieo i?ioean?a noathoue iaaoaeoeai?, ooo aeiaiaeeoueny caa?oaoeny
aei ni?iuaieo iaoiae?a, yeeie ca ?aooiie ao?aoe oi?aa?naeue-iino?,
aaea?oueny ?ica’ycaoe eiie?aoia eiei caaea/ cia/ii i?ino?oa. Iaeei ?c
oaeeo iaoiae?a, ui ioiieth? ii??aiyii oe?iea eiei caaea/, ? iaoiae
ei?aeoe?? ca na?aaei?i cia/aiiyi, aea a?i iaiaaeaiee ci?iieie, ui ia
i?noyoue iino?eieo neeaaeiaeo.

Iaoiae iiaoaeiae iiaeaeae /ooeeainoae aei ii/aoeiaeo oiia ? iaoiae
ei?aeoe?? ca na?aaei?i cia/aiiyi i?iiiiothoueny iaie ye iniiai? iaoiaee
?ic?aooieo onoaeaieo aeaeo?iiaai?oieo iie?a. Oe? iaoiaee a iaoaiaoe/iiio
aniaeo? noaiiaeyoue aeaioi/eiao e?aeiao caaea/o aeey cae/aeieo
ia-e?i?eieo aeeoa?aioe?aeueieo ??aiyiue, yea ? cia/ii neeaaei?oa ca
caaea/o Eio?, ine?eueee ooo ia i?ioean iaeeaaea?oueny aeiaeaoeiaa oiiaa
ia??iaee/-iino?.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa
aeeiioaaeany a ?aieao iaoeiai-oaoi?/ii? i?ia?aie «?aaeeie ?iaioe
aeaeo?iiinoa/aeueieo nenoai ? iaoiaee iioei?caoe?? ?o ?iaioe» Eooeueeiai
aea?aeaaiiai oaoi?/iiai oi?aa?neoaoo.

Iaoa oa caaea/? aeine?aeaeaiiy. ?ic?iaea iaoiae?a iaoaiaoe/iiai
iiaeaethaaiiy i?inoi?iaeo caaea/ aeaeo?iaeeiai?ee oa ciaoiaeaeaiiy
ia??iaee/ieo ?ica’yce?a ?o iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue c
/anoeiieie iio?aeieie e nenoai ci?oaieo iae?i?eieo aeeoa?aioe?aeueieo
??aiyiue c /anoeiieie ? cae/aeieie iio?aeieie, ye? a?oioothoueny ia
caaaeuei?e oai??? iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue.

Aeey aeinyaiaiiy oe??? iaoe iaiao?aeii ?ica’ycaoe oae? caaea/?.

1. Aaeaiooaaoe iaoiaee ?ica’ycaiiy aeaioi/eiaeo e?aeiaeo caaea/ aei
iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue c /anoeiieie iio?aeieie ? ia
nenoaie ci?oaieo iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue ?c cae/aeieie e
/anoeiieie iio?aeieie.

2. ?ic?iaeoe aeai?eoie ciaoiaeaeaiiy ia??iaee/ieo ?ica’yce?a iae?i?eieo
aeeoa?aioe?aeueieo ??aiyiue c /anoeiieie iio?aeieie ? nenoai ci?oaieo
iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue ?c cae/aeieie e /anoeiieie
iio?aeieie.

3. ?ic?iaeoe aeai?eoie ciaoiaeaeaiiy ia??iaee/ieo ?ica’yce?a nenoai
iae?i?eieo noaoe?iia?ieo ? ianoaoe?iia?ieo ??aiyiue c /anoeiieie
iio?aeieie.

4. Cae?enieoe i?ia?aiio ?aae?caoe?th ia i?eeeaaeao ?ica’ycaiiy
i?inoi?iaeo caaea/ aeaeo?iaeeiai?ee .

Iaoeiaa iiaecia ?iaioe. Aia?oa:

— ?ica’ycaii aeaioi/eiao t-ia?iiaee/io iaeiiaeii?io i?inoi?iao caaea/o
aeaeo?iaeeiaiiee aeey iaeiiieieo aeeoa?aioeiaeueieo ?iaiyiue
eaacinoaoeiiia?iiai aeaeo?iiaai?oiiai iiey o oa?iiaai?oiiio na?aaeiaeu?;

— ?ica’ycaii aeaioi/eiao t-ia?iiaee/io aeaiaei??io i?inoi?iao caaea/o
aeaeo?iaeeiaiiee aeey iaeiiieieo aeeoa?aioeiaeueieo ?iaiyiue
eaacinoaoeii-ia?iiai aeaeo?iiaai?oiiai iiey a nooeieueiiio
oa?iiaai?oiiio oi?i;

— ?ica’ycaii aeaioi/eiao t-ia?iiaee/io aeaiaeii?io i?inoi?iao caaea/o
aeaeo?iaeeiaiiee aeey ci?oaieo iae?i?eieo aeeoa?aioeiaeueieo ?iaiyiue
ae?inaey;

— ?ica’ycaii aeaioi/eiao t-ia?iiaee/io aeaiaeii?io i?inoi?iao caaea/o
aeey nenoaie iaeiiieieo noaoe?iia?ieo ? ianoaoe?iia?ieo
aeeoa?aioe?aeueieo ?iaiyiue aeaeo?iiaai?oiiai iiey a eaiiiiaaiiio
oa?iiaai?oiiio oi?i.

Iaoiaee aeine?aeaeaiiy. Oai?aoe/i? aeineiaeaeaiiy a?oioothoueny ia
caaaeuei?e oai??? iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue c /anoeiieie oa
cae/aeieie iio?aeieie, ??aiyiiyo eaacinoaoeiiia?iiai aeaeo?iiaai?oiiai
iiey a eiiieieo i iaeiiieieo na?aaeiaeuao, /enaeueieo iaoiaeao
?ica’ycaiiy iaeiiieieo aeeoa?aioeiaeueieo i aeaaa?a?/ieo ?iaiyiue.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a:

— eiii’thoa?ii i?ia?aie ?ica’ycaiiy aeaioi/eiaeo t-ia?iiaee/ieo
e?aeiaeo caaea/ aeaeo?iaeeiaiiee a nooeieueieo i eoneiai-iaeii?iaeieo
iaeiiieieo na?aaeiaeuao aeaee ciiao ?ica’ycaoe caaea/? aiaeico onoaeaieo
ia?iiaee/ieo i?ioeania aeaeo?ioaoi?/ieo i?eno?i?a;

— cai?iiiiiaaii aeai?eoie ?ica’ycaiiy aeaioi/eiaeo t-ia?iiaee/ieo
e?aeiaeo caaea/ aeaeo?iaeeiai?ee aeathoue ciiao aiae?coaaoe onoaeai?
i?ioeane a ?ioeo oice/ieo iieyo — iaoaii/ieo, oaieiaeo oiui.

Iniaenoee aianie aaoi?a. On? iniiai? iieiaeaiiy, ui noaiiaeyoue nooue
aeena?oaoe??, io?eiai? aaoi?ii naiino?eii. O ni?eueieo ioae?eaoe?yo
aaoi?o iaeaaeeoue: oi?ioaaiiy e?aeiai? caaea/? aeaeo?iiaai?oiiai iiey
[2,3], ?ic?aooiie onoaeaiiai i?ioeano a nooe?eueiiio oi?i?ae? [4],
?ic?aooiie aeaeo?e/iiai iiey a a?oio? [6], iien aeaeo?iiaai?oiiai
i?ioeano a oiie?e noaeaa?e ieanoei? [7], canoinoaaiiy e?i?eieo
ia?aoai?aiue ? iiaoaeiaa ??cieoeaaeo oaaeii?a aaeoi?-iioaioe?aeo
aeaeo?iiaai?oiiai iiey [8], e??i oiai, a on?o i?aoeyo aaoi? aeae?aa i
iaa?oioiaoaaa aeioeieueii /enaeueii iaoiaee, i?eeiaa o/anoue o iiaoaeia?
aeai?eoi?a ? i?ia?ai.

Ai?iaaaeaeaiiy ?acoeueoao?a ?iaioe. ?acoeueoaoe ?iaioe aeei?enoai? o
a?aeae?e? IAeA-1 IAI «Iao?ieia?y», i. Oa?e?a, ia aoai? i?iaeooaaiiy
?iai/iai aoaeiia aia?aaoe/ii? ina?oeaiino? niiy/iiai aei?ii?ithaaiiy a
oaeiae o IAeI-46 IAE «Ee?anueeee ?inoeooo aaoiiaoeee» ia aoai?
i?iaeooaaiiy nenoai ea?oaaiiy e ae?aaiinoeee i?ieaoieie noaiaie .
Oai?aoe/i? ?acoeueoaoe ai?iaaaeaeai? a iaa/aeueiee i?ioean o AeO
«Euea?anueea iie?oaoi?ea».

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? iieiaeaiiy oa ?acoeueoaoe
aeena?oaoe?eii? ?iaioe aeiiia?aeaeenue ? iaaiai?thaaeenue:

— Oeiea iieiaeeo o/aieo «Aeaeo?iiaoaii/ii e iaiiai?iaiaeieeiai
ia?aoai?thaa/i aeaeo?e/ii? aia?ai?”. — E?ei, Aeoooa, aa?anaiue, 1989;

— Oe?a?inueea eiioa?aioeiy “Iiaeaethaaiiy e aeineiaeaeaiiy noieeinoi
nenoai”, Ee?a, o?aaaiue, 1996;

— The 2-nd International Modelling School. — Crimea, Alushta, Autumn’97;

— IV srodowiskowa konferencja matematyczna. — Rzeszow, 1997;

— The 3-rd International Modelling School. — Crimea, Alushta, Autumn’98.

Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?? iioae?eiaaii 8 iaoeiaeo i?aoeue
(2 aac ni?aaaoi??a), c ieo 5 noaoae o oaoiaeo aeaeaiiyo Oe?a?ie, 1
aeiao?ae.

No?oeoo?a oa ia’?i ?iaioe. ?iaioa ia? anooi, 4 ?icae?ee, i?aenoiie e
nienie e?oa?aoo?e 95 iaca. ? 33 ?en. oa aeiaeaoie, ?acii 130 noi?.
Iniiaiee oaeno caeia? 118 noi?. Nienie e?oa?aoo?e caeia? 9 noi?. ?
aeiaeaoie — 3 n.

Iniiaiee ciIno aeena?oaoeIIIniiaiee ciIno aeena?oaoeII

O anooi? iaa?oioiaaii aeooaeuei?noue, iaoeiao iiaecio oa i?aeoe/io
oe?ii?noue ?iaioe, noi?ioeueiaaii iaoo aeine?aeaeaiue.

O ia?oiio ?icae?e? iiaeaii iaea?aeai? a ?acoeueoao? ii?aoethaaiiy
e?oa?aoo?e iniiai? oai?aoe/i? iieiaeaiiy, ia yeeo a?oioothoueny
iaoaiaoe/i? ?acoeueoaoe ianooiieo ?icae?e?a. I?eaaaeaii ??aiyiiy
eaac?noaoe?iia?iiai aeaeo?iiaai?oiiai iiey a eoneiai-iaeii??aeiiio
ai?cio?iiiiio iae?i?eiiio na?aaeiaeu?, a oaeiae ?o i?inoi?iai-/ania?
aeene?aoeciaai? aiaeiae, iaea?aeai? ca a?aeiieie iaoiaeaie i?inoi?iai?
oa /aniai? aeene?aoecaoe??. Iiaeathoueny iniiai? iaoiaee ?ica’ycaiiy
aeaioi/eiaeo e?aeiaeo caaea/ cae/aeieo iae?i?eieo aeeoa?aioe?aeueieo
??aiyiue.

??aiyiiy aaeoi??a eaac?noaoe?iia?iiai aeaeo?iiaai?oiiai iiey a
nooe?eueiiio iae?i?eiiio ai?cio?iiiiio na?aaeiaeu? iathoue aeaeyae
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``&???&??yyyy?????Ayyy3/4yyy &??

?? ???&? ?MathType??`????u@th??????aea H, E — aaeoi?e
iai?oaeaiinoae iaaiaoiiai e aeaeo?e/iiai iie?a; B — aaeoi? iaai?oii?
?iaeoeoe?e; — ae?aaiiaeueia iao?eoey noaoe/ieo ?aeaeoeaiinoae; ?-
ae?aaiiaeueia iao?eoey ieoiieo iaai?oieo iii??a; t — /an.

A?aeiia?aei? (1) ??aiyiiy aaeoi?-iioaioe?aeo A iaaoaathoue aeaeyaeo

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?? ???&? ?MathType??`????u@th??????I?e oeueiio (1),(2) ia?aaeaa/a?
caaeai? ii/aoeia? e e?aeia? oiiae.

Aeaeo?iiaai?oia iiea a oeooiaaiiio oa?iiaaiaoeeo aea?aaeaioo?oueny
aeayeei ai?cio?iiiei iaeii??aeiei na?aaeiaeuai.

I?inoi?iai aeene?aoeciaai? ??aiyiiy (1) ca iaoiaeaie ne?i/aiieo
??cieoeue aai ne?i/aiieo aeaiaio?a caieno?ii o iao?e/iiio aeaeyaei

wmetafile8? ??O???G????????
???????????yyy????.????1?????? ???????
`a???&??yyyy?????Ayyy?yyy ???? ???&? ?MathType????
???u?????????»????-?????T@????T???u@th??????aea BD, HD ,
ED- eieiiee i?iaeoeie aaeoi?ia B, H, E o aioo?ioiio aoceao; HAD —
eieiiea i?iaeoeie aaeoi?a H o a?aie/ieo aoceao; C1-C4 — iao?eoei
i?icoi?iai? aeene?aoecaoei?; — iao?eoey noaoe/ieo ?aeaeoeaiinoae. ??
oi?io?ii aaciina?aaeiuei c aeaiaioia iao?eoe? N aiaeiiaiaeii aei
iiiaeeie aoceia i?inoi?iai? nioee.

Aiane?aeie i?inoi?iai? aeene?aoecaoei? (2) io?eio?ii

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???u?????????»????-?????T@????T???u@th??????aea AD ,
AAD- eieiiee eiiiiiaio?a aaeoi?a A aiaeiiaiaeii aei e?eueeino?
aioo?ioiio ? a?aie/ieo aoceia i?inoi?iai? nioee; C6-C7 — iao?eoei
i?inoi?iai? aeene?aoecaoei?.

Aeeoa?aioe?aeuei? ??aiyiiy (3), (4) caieno?ii a caaaeueiiio aeaeyae?

wmetafile8? ??T???+????????
???????????yyy????.????1?????? ???????
``???&??yyyy?????Ayyy?yyy ???? ???&? ?MathType????
???u?????????»????-?????T@????T°???u@th??????aea X —
eieiiea iaaiaeiieo.

?ioaa?o?ii (5) caeaaeii a?ae aei?noeino? ??aiyiue ca yaieie aai iayaieie
iaoiaeaie. O aeiaaeeo canoinoaaiiy iayaieo iaoiae?a aeene?aoeciaai?
?iaiyiiy ?oca’yco?ii ioa?aoeieieie iaoiaeaie ioeueiaiai (c iie?auaiiyi
ca?aeiino? ca iaoiaeii aa?oiuei? ?aeaenaoe??) aai ia?oiai ii?yaeeia.

?icaeyiaii iniiai? iaoiaee ?ica’ycaiiy aeaioi/eiai? e?aeiai? caaea/?
aeey iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue (5). I?eionoeii, ui inio? ??
ia?iiaee/iee ?ica’ycie c ia?iiaeii T. Oea icia/a?, ui ia?aoiaeia
?aaeoeiy aiaenooiy. Ciaeaeaii oaeee ii/aoeiaee noai X(0), eio?ee i?e
iioaa?oaaiii (5) ia iioa?aaei /ano aiae 0 aei O, aeaa ae iiaeeeainoue
io?eiaoe aaciina?aaeiuei ia?iiaee/iee ?ica’ycie, ui caaeiaieueiya ae
e?aeiaie oiiai

wmetafile8? ?????????????
???????????yyy????.????1?????? ???????
` ???&??yyyy?????Ayyy3/4yyy`??

?? ???&? ?MathType??`????u@th???????iaiyiiy (5) c e?aeiaith oiiaith
(6) noaiiaeyoue aeaioi/eiao e?aeiao caaea/o aeey cae/aeieo
aeeoa?aioeiaeueieo ?iaiyiue.

Aeaioi/eiaa e?aeiaa caaea/a iaaaaaoi neeaaeiioa ca caaea/o Eioi. Ooo ia
ii/aoeiai oiiae iaeeaaea?oueny aei?noea oiiaa — aiie iiaeiii aeeeth/aoe
ia?aoiaeio ?aaeoeith, oiaoi aeaoe iiaeeeainoue aaciina?aaeiuei aaieoe o
ia?iiaee/iee ?aaeei, iaieiath/e ia?ao?aeiee. Oaei ii/aoeia? oiiae ?
iaaiaeii?. ?o ciaoiaeaeaiiy iia’ycaia c ?ica’ycaiiyi o?ainoeaiaeaioieo
iaeiiieieo aeaaa?a?/ieo ?iaiyiue (6). Iaa?aeiiei o oeueiio ?iaiyii? ?
noiaiaoeue ooeaieo ii/aoeiaeo oiia O(0).

?iaiyiiy (6) iaceaathoue ?iaiyiiyi oeiei, aai oeieueiaith ooieoei?th.
?ica’yco?ii eiai ?oa?aoe?eiei iaoiaeii Iuethoiia

wmetafile8? ??a???c????????
???????????yyy????.????1?????? ???????
@????&??yyyy?????Ayyy¤yyyA ??ae?? ???&?
?MathType???????u*yy?????Iao?eoeth sseiai F X(0) io?eio?ii
aeeoa?aioeithaaiiyi (6) ii X(0)

wmetafile8? ?????)????????
???????????yyy????.????1?????? ???????
` ???&??yyyy?????Ayyy3/4yyy`??

?? ???&? ?MathType??`????u@th??????i?e/iio

wmetafile8? ??i???5????????
???????????yyy????.????1?????? ???????
``???&??yyyy?????Ayyy3/4yyy ??

?? ???&? ?MathType??`? ???u?????????»????-?????B?m???Y
???u@th?????? Ooieoeiy (9) — iao?eoey iiiiae?iii?. ?? aecia/a?ii ca
aa?iaoeieiei ?iaiyiiyi, io?eiaiei c ?iaiyiiy (5),

wmetafile8? ??AE???7????????
???????????yyy????.????1?????? ??????? ?A
???&??yyyy?????Ayyy?yyy? ??2?? ???&? ?MathType??a?
???u?????????»????-?????T@????TY???T5???TOe
???u@th??????Ia k-?e ioa?aoei? oi?ioee Iuethoiia aiii iiaeeyaa?
noiiniiio iioaa?oaaiith c (5) ia iioa?aaei /ano O. Iao?eoey iiiiae?iii?
? ii nooi iao?eoeath /ooeeainoae aei ii/aoeiaeo oiia. Oiio ?iaiyiiy (10)
o?aeoo?oueny ye iiaeaeue /ooeeainoi aei ii/aoeiaeo oiia.

?c caaaeueieo iaoiae?a, e??i iaoiaeo iiaoaeiae iiaeae? /ooeeainoae aei
ii/aoeiaeo oiia, ne?ae iacaaoe aeno?aiieyoeieiee ? a?aae??ioiee iaoiaee.
Ia?oee c ieo ?icaeyiooi, a ae?oaee ?c-ca eiai neeaaeiino? iiouaii.

sseui o?ce/ia na?aaeiaeua ia? neiao?e/ii aiaeiinii ii/aoeo eii?aeeiao
oa?aeoa?enoeee, a aeioooaaeueii neee ? iaeii?? i oi?? ae /anoioe, oi o
oaeiio aeiaaeeo aeioeieueii canoinoaaoe aieueo i?inoee iaoiae — iaoiae
ei?aeoe?? ca na?aaei?ie cia/aiiyie (ia?aiee aeai?eoi)

wmetafile8? ??©???U????????
???????????yyy????.????1?????? ???????
?@???&??yyyy?????Ayyy?yyy???8?? ???&?
?MathType??`????u@th??????aea Xmax, Xmin — coiaioe? iaeneiaeueieo i
iiiiiaeueieo cia/aiue ciiiieo ia ia??iae?. Uia io?eiaoe oei cia/aiiy ia
e-e ioa?aoei?, o?aaa iioaa?oaaoe (5) o oeeo aea iaaeao.

O aaaaoueio i?aeoe/ieo caaea/ao oiiae canoiniaiino? ioa?aoeieii? oi?ioee
(11) caaeiaieueiythoueny ? oiio aiia ia? aeinoaoiuei oe?iea
canoinoaaiiy. Oae, aiia ? canoiniaiith o aeiaaeeo aa?iii?/iiai
aeaeo?iiaai?oiiai iiey. Ia?aiee aeai?eoi — iaei?inoioee c aiaeiieo
iaoiaeia i?enei?aiiai iiooeo aeiooaieo ia?iiaee/ieo ?aaeeiia.

Iaoiaee i?enei?aiiai iiooeo aeiooaieo ia?iiaee/ieo ?aaeeiia i?eaeaoi?
oaeiae aeey onoaeaieo iinoieieie iie?a.

O ae?oaiio ?icae?e? ?ica’ycothoueny iaeiiaei??i? i?inoi?ia? aeaioi/eia?
e?aeia? caaea/? aeey aeeoa?aioe?aeueieo ??aiyiue c /anoeiieie iio?aeieie
e ci?oaieo aeeoa?aioe?aeueieo ??aiyiue c /anoeiieie oa cae/aeieie
iio?aeieie. Ciaoiaeeoueny onoaeaiee i?ioean o noaeaaiio oiieiio
oa?iiaai?oiiio eeno?, oeooiaaiiio oa?iiaai?oiiio oi?? oa oi?i?aeaeueiiio
ae?inae?i?e aa?iii?/ieo ao?aeieo neaiaeao.

?ic?aooieia? ??aiyiiy aeaeo?iiaaiaoiiai iiey (3) o oiieiio noaeaaiio
eeno? caieno?ii a aeaea?oiaeo eii?aeeiaoao

wmetafile8? ??u???=????????
???????????yyy????.????1?????? ??????? ? 
???&??yyyy?????Ayyy¬yyy` ??¬?? ???&? ?MathType??
???u?????????»????-?????t@????ts???tO???te???t
???tAE???u@th?????? Iaeanoue ?ioaa?oaaiiy (12): aea d —
oiaueia eenoa.

O aeena?oaoe?? i?eaaaeaii oaeiae ??aiyiiy aaeoi?iiai iioaioe?aeo.

O ?acoeueoao? i?inoi?iai? aeene?aoecaoe?? (12) i?eoiaeeii aei (3)-(5).

??aiyiiy oe?e? (6 ) aoaea

wmetafile8? ??y???A????????
???????????yyy????.????1?????? ??????? `
???&??yyyy?????Ayyy3/4yyya??

?? ???&? ?MathType??`????u@th???????ica’yco?ii (13) iaoiaeii
Iuethoiia( 7). I?e oeueiio (10) aoaea

wmetafile8? ??????1????????
???????????yyy????.????1?????? ??????? ``
???&??yyyy?????Ayyy?yyy ???? ???&? ?MathType????
???u?????????»????-?????T@????TY???u@th?????????,?w????2
Awmetafile8? ??I???????????? ??????? i?!???
???????yyy????????C
?I???i?!????i?!????(???!??i?????????%??Ae??Ae??????????????yyy?y
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyythyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyythyyyyyyyyyyyyyyyyyyyyyyyyy
yyyyyyyyyyyyy?yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
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yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
yyyyyyyyyyyyyyyyyyyyyyyyyyyyyyueyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
a?yyyyyyyyyyyyyythyyyyyyyyyyyyyyyyyyyyyAueyyyyyyyyyyyyyyyyyyyyyyyyyy
yyyyyyyyyy?en. 1. ?ic?aooieia? e?ea? onoaeaieo cia/aiue iaai?oii?
?iaeoeoe?? a /an? i?e ??cieo cia/aiiyo i?inoi?iai? eii?aeeiaoe z = 0
(1), z = 0,01 i (2), z = 0,02 i (3) o oiieiio noaeaaiio eeno? a ?aaeei?
caaeaii? ia eiai iiaa?oi? ?iaeoeoe??

aea wmetafile8? ??(??? ????????
?????????????yyy????.??????1?????? ???????
@A???&??yyyy?????Ayyy?yyy???o?? ???&? ?MathType??P?
???u?th??????Caaea/a ?ica’ycoaaeany a ?aaeeiao caaeaii? ?iaeoeoe?? ia
iiaa?oiyo iaai?oiiai eenoa oa iaai?oiiai iioieo.

?ioaa?oaaiiy ??aiyiue cae?enithaaeiny ca yaiei ? iayaiei iaoiaeaie
Aeea?a. I?e ?ioaa?oaaii? iayaiei iaoiaeii aeei?enoiaoaaany iaoiae
i?iaiiee ia i?aenoaa? a?aeiieo ?aeo?aioieo ni?aa?aeiioaiue. ?acoeue-oaoe
?ic?aooieo iieacaii ia ?en. 1.

Ae?oaith ?ica’ycaiith caaea/ath ? aeaioi/eiaa e?aeiaa caaea/a aeey
??aiyiue c /anoeiieie iio?aeieie ca e?eaie?i?eiith eii?aeeiaoith —
aeaeo?iiaai?oiee i?ioean o oeooiaaiiio oi?i?aeaeueiiio ina?ae?.
?ic?aooieia? ??aiyiiy a oeee?iae?e/ieo eii?aeeiaoao aeei?enoai? o
aeaeyae?

wmetafile8? ?????m????????
???????????yyy????.????1?????? ??????? 
a???&??yyyy?????Ayyy¬yyy ??I?? ???&? ?MathType??
???u?????????»????-?????”@????”s???”O???”/???”
L???”e???”*
???”???”L???”a???”¤???”^???u@th??????

Iaeanoue ?ioaa?oaaiiy (15): wmetafile8? ??!??? ????????
?????????????yyy????.??????1?????? ???????
?`???&??yyyy?????AyyyAyyy ??A?? ???&? ?MathType??P?
???u?th??????O?aoueith ?ica’ycaiith caaea/ath ? aeaioi/eiaa e?aeiaa
caaea/a aeey ci?oaieo aeeoa?aioe?aeueieo ??aiyiue ?c cae/aeieie e
/anoeiieie iio?aeieie — aeaeo?iiaai?oiee i?ioean o oi?i?aeaeueiiio
ae?inae? ia i?eeeaae? ??aiyiue eaac?noaoe?iia?iiai aeaeo?iiaai?oiiai
iiey e ??aiyiue ??aiiaaae iai?oa ? aeaeo?i?oo?eieo nee iaiioee
iaiaai?/oaaiiy

wmetafile8? ??¬???1????????
???????????yyy????.????1?????? ???????
`????&??yyyy?????Ayyy?yyy@???? ???&? ?MathType????
???u?????????»????-?????T@????TTH???u„y????aea x —
aeayeee noaeee eiao?oe??io, caeaaeiee a?ae i?inoi?iaiai e?ieo
aeene?aoecaoe??;

wmetafile8? ?????#????????
???????????yyy????.????1?????? ??????? a?
???&??yyyy?????Ayyy?yyyA??’?? ???&? ?MathType??
???u?????????»????-?????T????T;???u@th??????i?e/iio a —
iaa?iaia ?iaeoeoeai?noue aeeneiaoe?? iaiioee; qk — eiao?oe??ioe oi?ioee
N?iiniia; — aeeoa?aioe?aeueia ?aeaeoeai?noue, cia/aiiy yei? ciaoiaeeii
ca aeeoa?aioe?aeueiith ?aeaeoeai?noth oa?iiaaiaoeea : , e — eiao?oe??io
ai?cio?iii?? eai?iiaaiiai ina?aey.

Noi?niiio ?ioaa?oaaiith i?aeeyaa? nenoaia ci?oaieo iae?i?eieo
aeeoa?aioe?aeueieo ??aiyiue (15), (16). O ?acoeueoao? i?inoi?iai?
aeene?aoecaoe?? iaaea?ii ?i oi?iaeueiiai aeaeyaeo (5) ca oiiae, ui
f(X,t) iaaeae? — O-ia??iaee/ia. Aeae? ia (5) iaeeaaea?ii oiiao
O-ia??iaee/iino? (6) ? canoiniao?ii ?oa?aoe?eio oi?ioeo (11).

O o?aoueiio ?icae?e? ?ica’ycothoueny aeaiaei??i? i?inoi?ia? caaea/?,
iia’ycai? c ?ic?aooieii onoaeaiiai aeaeo?iiaai?oiiai iiey a nooe?eueiiio
oi?? oa eai?iiaaiiio oi?? ye eoneiai-iaeii??aeiiio na?aaeiaeu?, a yeiio
/a?aothoueny oa?iiaai?oi? oa iaiaai?oi? oa?e.

?icaeyiaii nii/aoeo aeaioi/eiao e?aeiao caaea/o ??aiyiue
aeaeo?iiaai?oiiai iiey a nooe?eueiiio oi?i?ae?.

Ia?o? aeaa ?ic?aooieia? ??aiyiiy (1) caieno?ii a oaeiio aeaeyae?

wmetafile8? ??<??????????? ???????????yyy????.????1?????? ???????  ????&??yyyy?????Ayyy¬yyyA??I?? ???&? ?MathType?? ???u?????????"????-?????”@????”s???”O???”e???” ‚???”› ???”` ???”: ???”‚ ???”???”U???””???”Y???”r???u@th??????Eiiiiia ioe aaeoi?a A iai?oaeaiino? aeaeo?e/iiai iiey ia/eneth?ii aaciina?aaeiuei ca inoaii?i ae?acii (1) wmetafile8? ??E???g???????? ???????????yyy????.????1?????? ??????? ?A???&??yyyy?????Ayyy?yyy?????? ???&? ?MathType?? ???u?????????"????-?????ta???toe???t>???tO???
t???t???t:???tI???t”???tN???u@th??????Iae
anoue ?ioaa?oaaiiy (18) iaiaaeaia ieiuath iiia?a/iiai ia?a??co o?ea
oi?i?aea, aai, aeoiaey/e c oiiae neiao??? ca aen?aeueiith eii?aeeiaoith,
— i?aieiuath oeueiai ia?a??co. E?aeia? oiiae acaeiaae ciai?oi?o
a?aieoeue oi?i?aea caaea?ii, aeoiaey/e ?c caeiio Aiia?a, a ?aaeei?
caaeaii? iaai?oi?oo?eii? neee.

I?inoi?iai-/aniai aeene?aoeciaaia aeeoa?aioe?aeueia ??aiyiiy (18) ca
iayaiei iaoiaeii Aeea?a iaaoaa? aeaeyaeo

wmetafile8? ??p???…????????
???????????yyy????.????1?????? ???????
`a2???&??yyyy?????Ayyy3/4yyy 2??

?? ???&? ?MathType??`????u@th??????
(20)

Iae?i?eia aeaaa?a?/ia ??aiyiiy (20) ?ica’yco?ii ?oa?aoe?eiei iaoiaeii
Iuethoiia (7) ca oiiae, ui wmetafile8? ?????? ????????
?????????????yyy????.??????1?????? ??????? ? 
???&??yyyy?????AyyyAyyy` ??A?? ???&? ?MathType??P?
???u?th?????? wmetafile8? ??u????????????
???????????yyy????.????1?????? ??????? 
????&??yyyy?????AyyyTHyyy@??th?? ???&?
?MathType??P????u@th??????aea

wmetafile8? ??????C????????
???????????yyy????.????1?????? ???????
?`???&??yyyy?????Ayyy?yyy ??8?? ???&?
?MathType??`????u@th?????? wmetafile8? ??’???K????????
???????????yyy????.????1?????? ??????? `@
???&??yyyy?????Ayyy3/4yyy? ??

?? ???&? ?MathType??`????u@th??????Iao?eoeth sseia? ciaoiaeeii a
?acoeueoao? aeeoa?aioe?thaaiiy (20) ii wmetafile8? ??“???!????????
?????????????yyy????.??????1?????? ???????
?a???&??yyyy????????Ayyyl ??A?? ???&? ?MathType??P?
???u?th?????? wmetafile8? ??y???I????????
???????????yyy????.????1?????? ??????? ?
???&??yyyy?????Ayyy?yyya??8?? ???&?
?MathType??`????u@th??????Nenoaio (21)-(24) ?ica’yco?ii iaoiaeii
i?inoi? ?oa?aoe??, aai iaoiaeii Yaonna. O ?acoeueoao? /iai ciaoiaeeii
eieiiee wmetafile8? ?????? ????????
?????????????yyy????.??????1?????? ???????
@a???&??yyyy?????Ayyy?yyy ??o?? ???&? ?MathType??P?
???u?th?????? ?ica’ycaiiy aeaioi/eiai? e?aeiai? caaea/? iia’ycaii,
ca?aeii c (6)-(10), c ia/eneaiiyi cia/aiiy iao?eoe? iiiiae?ii??
wmetafile8? ????? ????????
?????????????yyy????.??????1?????? ???????
?`???&??yyyy?????Ayyy·yyy ??7?? ???&? ?MathType??p?
???u?th??????wmetafile8? ??????U????????
???????????yyy????.????1?????? ???????
?`%???&??yyyy?????Ayyy?yyy %??8?? ???&?
?MathType??`????u@th??????Aeeoa?aioe?thth/e (20) ii , iaea?aeo?ii
ooeaio iao?eoeth sseia?

wmetafile8? ??R???C????????
???????????yyy????.????1?????? ???????
?`???&??yyyy?????Ayyy?yyy ??8?? ???&?
?MathType??`????u@th??????sse aa/eii i?aa? /anoeie (24) ? (26)
ca?aathoueny.

I?aenoaaeyth/e (25), (26) a ?oa?aoe?eio oi?ioeo (21), iaea?aeeii ciiao
nenoaio e?i?eieo aeaaa?a?/ieo ??aiyiue aeaeyaeo (21), aea ooo ia
a?aei?io a?ae (22), (24) ia?ii

wmetafile8? ??o???A????????
???????????yyy????.????1?????? ??????? `
???&??yyyy?????Ayyy3/4yyya??

?? ???&? ?MathType??`????u@th?????? wmetafile8?
??»???9???????? ???????????yyy????.????1??????
??????? ?a???&??yyyy?????Ayyy?yyy ??8?? ???&?
?MathType??`????u@th??????wmetafile8? ??O???????????? ???????
I???? ???????yyy????????C
?I???I?????I?????(?????I?????????
??Ae??Ae??????????????yyy?yyyssyyyyyyyyyyyyyyyyyyyyyyyyyyyy????yyyssy
yyyyyyyyyyyyyyyyyyyyyyyyyyy????yyyssyyyyyyyyyyyyyyyyyyyyyyyyuyyy????yyys
syyyyyyyyyyyyyyyy?yyyyyyyuyyy????yyyssyyyyyyyyyyyyyyyy?yyyyyyyuyyy????yy
yssyyyyyyyuyyyyyyyy?yyyyyyyuyyy????yyyssyyyyyyyuyyyyyyyy?yyyyyyyuyyy????
yyyssyyyyyyyuyyyyyyyy?yyyyyyyuyyy????yyyssyyyyyyyuyyyyyyyy?yyyyyyyuyyy??
??yyyssyyyyN???????????????????yyy????yyyA??????????
?oyy?yyyyyyyuyyy????yyyssyyyyyyyuyyyyyyyy?yyyyyyyuyyy????yyyssyyyyyyyuy
yyyyyyy?yyyyyyyuyyy????yyyssyyyyyyyuyyyyyyyy?yyyyyyyuyyy????yyyssyyyyyyy
uyyyyyyyy?yyue?yyyuyyy????yyyssyyy?yyyuyyy?yyyyyyyyyyyyyyy????yyyssyyys
syyyyyyyyyyyyyyyyyyyyyyy????yyyssyyyssyyyyyyyssyyyyyyyy?yyyyyyy????yyys
syyyssyyyyyyyssyyyyyyyy?yyyyyyy????yyyssyyyiyyyyyyyIyyyyyyyy·yyyyyyy????
yyyssyyyoyyyyyyyoyyyyyyyy·yyyyyyy????yyyssyyy?en. 2. ?ic?aooieia? e?ea?
iaai?oii? ?iaeoeoe?? ye ooieoe?? /ano a oi/oe? iiia?a/iiai ia?a??co
oi?i?aea c eii?aeeiaoaie r = 0,522 i; z = 0,0167 i ia o?ueio ?oa?aoe?yo
?ica’ycaiiy aeaioi/eiai? e?aeiai? caaea/?.

Caa?oa?ii oaaao ia a?aei?ii?noue ??aiyiue (21) aeey wmetafile8?
??“???!???????? ?????????????yyy????.??????1??????
??????? ?a???&??yyyy????????Ayyyl ??A?? ???&?
?MathType??P? ???u?th??????Ia ?en. 2 iieacaiee ia?aa?a o /an? iaai?oii?
?iaeoeoe?? a iaeiiio c aoce?a i?inoi?iai? n?oee ia aeaio ?oa?aoe?yo
oi?ioee Iuethoiia, ui i?ecaaee aei onoaeaiiai i?ioeano. sse aa/eii, ia
eiaei?e c ?oa?aoe?e ?ica’yco?oueny caaea/a Eio? ia /aniaiio ?ioa?aae?
iaeiiai ia??iaeo T. O?aoy ?oa?aoe?y — ? aeania onoaeaiee i?ioean,
iaea?aeaiee ye ?acoeueoao ?ica’ycaiiy aeaioi/eiai? e?aeiai? caaea/?. Ii
e?ea?e A(t) aa/eii, ui nooo?aa ooi/iaiiy a?aeaoeiny aaea ia ia?o?e
?oa?aoe??. Ia ae?oa?e aiii iaeaea iaiii?oia aeey iaica?i?iiai iea.

Ianooiia aeaioi/eiaa e?aeiaa caaea/a ? a?eueo neeaaeia — oea aeiaaeie
nenoaie noaoe?iia?ieo ? ianoaoe?iia?ieo aeeoa?aioe?aeueieo ??aiyiue.

?icaeyiaii iaeio c iaeneeaaei?oeo i?inoi?iaeo caaea/ aeaeo?iaeeiai?ee —
?ic?aooiie aeaeo?iiaai?oieo i?ioean?a o eai?iiaaieo ina?aeyo. Aei
oeueiai /ano eai?iiaai? iaai?oi? ina?aey, ui neeaaeathoueny c oa??a
oa?iiaai?oieo eeno?a ? ?cieyoe?eieo i?ii?aee?a, ie aea?aaeaiooaaee
nooe?eueiei ai?cio?iiiei na?aaeiaeuai. Aea ? ?yae caaea/, aea oaeee
i?aeo?ae iaaeiionoeiee, iai?eeeaae, i?e aeine?aeaeaii? ao?ao i?e
anaiiaeeeaeo iioeiaeaeaiiyo iaai?oii?iaiaea — ei?ioeeo caieeaiiyo
eeno?a, /anoeiaeo aai iiaieo, ?ici?anoaaiiyo oiui. Iniaeeai
caaino?th?oueny oey i?iaeaia i?e a?aooaaii? oaiia?aoo?ieo yaeu. Oe?eaai,
ui ca oa?aeoa?ii aeaeo?iiaai?oiiai i?ioeano a iioeiaeaeaieo
iaai?oii?iaiaeao ooo/i? iae?iii? ia?aae? iiaeooue oni?oii cae?enithaaoe
?o ae?aaiinoeeo.

Neeaaei?noue iaoaiaoe/iiai iiaeaethaaiiy ooo coiiaeaia a ia?oo /a?ao
aeaiia aaaeeeaeie oaeoi?aie. Ia?oee c ieo oea oa, ui i?ioean iieno?oueny
ia aeeoa?aioe?aeueieie ??aiyiiyie ca /anii, ye oea iaei i?noea a on?o
?icaeyiooeo aei oiai caaea/ao, a coaoe?iia?ieie. Ae?oaee c ieo aeiaaa?
canoinoaaiiy aeoaea ae??aii? i?inoi?iai? n?oee, a oea, a naith /a?ao,
iaeeaaea? aei?noe? iaiaaeaiiy ia aea?? /aniaiai e?ieo caaeey
caaacia/aiiy no?eeino? ia/enethaaeueiiai i?ioeano.

?icaeyiaii ana oa ae eai?iiaaia oi?i?aeaeueia ina?aey, caoaeaeaia
neioni?aeaeueiei no?oiii. A?aei?ii?noue aeaii? caaea/? a?ae ?icaeyiooi?
a o?aoueiio ?icae?e? iieyaa? a oiio, ui ooo ie a?aeiiaey?iiny a?ae
aea?aaeaiooaaiiy ina?aey, a ?icaeyaea?ii ?aaeueio eai?iiaaio no?oeoo?o.

Ioaea, a iaeano? ?ioaa?oaaiiy, iaiaaeai?e iiia?a/iei ia?a??cii o?ea
oi?i?aea, /a?aothoueny oa?i- e iaiaaiaoeee. O cii? oa?iiaaiaoeea
o?ce/iee i?ioean iieno?oueny ana oeie ae aeeoa?aioe?aeueieie ca /anii
??aiyiiyie (18), (19). Aeae? caa??aathoue neeo an? ?aooa ae?ac?a. A oea
cia/eoue, ui e?aeia? oiiae oa aeene?aoeciaai? ca /anii ??aiyiiy
aeaeo?iiaai?oiiai iiey ia ci?iyoueny. Aea ooo aeieeathoue aeiaeaoeia?
aioo??oi? e?aeia? oiiae, ui iathoue i?noea ia iaae? oa?iiaaiaoeea oa
?cieaeo

wmetafile8? ??µ???=????????
???????????yyy????.????1?????? ??????? ??
???&??yyyy?????Ayyy»yyyA??»?? ???&? ?MathType??
???u?????????»????-?????t???t???u@th??????O cii?
iaiaaiaoeea, aiaeii/an a?i ? ?cieyoi?ii, wmetafile8? ??y????
???????? ?????????????yyy????.??????1?????? ???????
aA???&??yyyy?????Ayyyayyy???A?? ???&? ?MathType??P?
???u?th?????? wmetafile8? ??????i????????
???????????yyy????.????1?????? ???????
 `???&??yyyy?????Ayyy¬yyy ??L?? ???&? ?MathType??a?
???u?????????»????-?????t@????tY???t

???to???t@???tO???t????tR
???t???t0???u@th??????aea wmetafile8? ??????? ????????
?????????????yyy????.??????1?????? ???????
?A???&??yyyy?????AyyyAyyy???A?? ???&? ?MathType??P?
???u?th?????? Noi?niiio ?ioaa?oaaiith i?aeeyaa? nenoaia
aeaaa?i-aeeoa?aioe?aeueieo ??aiyiue (18), (19), (29), (30). Ine?eueee ia
aioo??oi?o a?aieoeyo eiiiiiaioe aaeoi?a A oa?ieyoue ?ic?ea, oi aeey
iaeiicia/iino? ?ica’yceo iaiao?aeii i?eeiyoe iaai? i??i?eoaoe. Ie
i?eeia?ii, ui ?iaeoeoe?th a a?aie/ieo aoceao aecia/aoeiaii ca
aeeoa?aioe?aeueieie ??aiyiiyie, c ianooiiei ia?a?aooieii ?? o oeueiio ae
aoce? a ciio iaiaaiaoeea ca?aeii c (29). O ?acoeueoao? i?inoi?iai?
aeene?aoecaoe?? iaea?aeo?ii nenoaio aeaaa?i-aeeoa?aioe?aeueieo ??aiyiue

wmetafile8? ??I???q????????
???????????yyy????.????1?????? ???????
 a???&??yyyy?????Ayyy»yyy ??[?? ???&? ?MathType??a?
???u?????????»????-?????t@????t wmetafile8?
??h???a???????? ???????????yyy????.????1??????
??????? `@???&??yyyy?????Ayyy3/4yyy???

?? ???&? ?MathType??`????u@th??????O (31), (32) ?iaeaene f ? 0
oeacothoue a?aeiia?aeii ia i?e/aoi?noue aei oa?i- ? iaiaaiaoeea.
Caieoaii nenoaio (31), (32) a caaaeueiiio aeaeyae?

wmetafile8? ??E???/????????
???????????yyy????.????1?????? ???????  ?
???&??yyyy?????Ayyy»yyyA??[?? ???&? ?MathType??a?
???u?????????»????-?????t@????tIa nenoaio (33) iaeeaaea?ii
oiiao t-ia??iaee/iino? e ?ica’yco?ii aeaioi/eiao e?aeiao caaea/o aeey
aeaaa?i-aeeoa?aioe?aeueieo ??aiyiue aeaeo?iiaai?oiiai noaio caoaeaeaiiai
eai?iiaaiiai oi?i?aeaeueiiai iaai?oiiai ina?aey ia i?aenoaa? ia?aiiai
aeai?eoio (11).

wmetafile8? ??O“????®“??????? ??????? ae?A???
???????yyy?????®“??C
?I???ae?A????ae?A????(???A??ae?????????#?’??’???????????????
??????? ?? ?
???????????????? ??

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?!!!?»»»?###?$$$?%%%?&&&?»’?(((?)))?***?+++?,,,?—?…?///?000?111?222
?333?444?555?666?777?888?999?:::?;;;?<<>>?????@@@?AAA?BBB?CCC?DDD
?EEE?FFF?GGG?HHH?III?JJJ?KKK?LLL?MMM?NNN?OOO?PPP?QQQ?RRR?SSS?TTT?UUU?VVV
?WWW?XXX?YYY?ZZZ?[[[?]]]?^^^?___?«`?aaa?bbb?ccc?ddd?eee?fff?ggg?hhh?iii
?jjj?kkk?lll?mmm?nnn?ooo?ppp?qqq?rrr?sss?ttt?uuu?vvv?www?xxx?yyy?zzz??||
|??~~~???????en.3. I?inoi?iaee ?iciiae?e iaai?o ii? ?iaeoeoe?? i?e t
= 0, 005c onoaeaiiai i?ioeano a o?e? iiia?a/iiai ia?a??co
oi?i?aeaeueiiai eai?iiaaiiai ina?aey

Ia ?en. 3 iieacaii ?acoeueoaoe ?ic?aooieo onoaeaiiai i?ioeano a
oi?i?aeaeueiiio ina?ae?, caoaeaeaiiio aa?iii?/iith iaa?oi?oo?eiith
neeith. ?aaeueia no?oeoo?a i?noeoue o?e aeaeo?ioaoi?/i? noaeaa? eenoe,
oiaueiith df = 2 ii ? aeaa i?ii?aeee ?cieyoe?eiiai eaeo d0 = 0,85 ii.
Aeaeo?ii?ia?aei?noue oa?iiaaiaoeea g = 2 106 Ni/i, oa?aeoa?enoeea
iaiaai?/oaaiiy eiai i?eeiaeany oaeith, yea iaaaaeaia a iiia?aaeiueiio
i?eeeaae?. Aaiiao?e/i? ?ici??e oi?i?aea: aioo??oi?e ?aae?on R1 = 0,1000
i; ciai?oi?e ?aae?on R2 = 0,107 i, aenioa a = 0,045 i. ?ici??e
i?inoi?iai? n?oee 55wmetafile8? ??F???? ????????
?????????????yyy????.??????1?????? ???????
``???&??yyyy?????Ayyy???? ??`?? ???&? ?MathType?? ?
???u?th??????1/4?????Symbol??ae*O|iwU|iw?giwae*??????-?? ???2
:?????y*????&??yyyy?????
???u??????1/4???I»System?????????????????????-???????
??????19, i?e/iio ca ?aae?aeueiith eii?aeeiaoith 55 aoce?a, ca
aen?aeueiith — 19. Ia??iaee/iee ?ica’ycie iaea?aeaii ca aea? ?oa?aoe??
oi?ioee (11).

O /aoaa?oiio ?icae?e? iienaii i?ia?aii? i?iaeoeoe iiaeaethaaiiy
onoaeaieo aeaeo?iiaai?oieo iie?a o i?inoi?iaeo caaea/ao
aeaeo?iaeeiai?ee. I?ia?aii? caniae noai?ai? c aeei?enoaiiyi
aeai?eoi?/ii? iiae Ms Fortran Pover Station 4.0 a iia?aoe?eiiio
na?aaeiaeu? Windows’95.

INIIAII ?ACOEUeOAOE ?IAIOEINIIAII ?ACOEUeOAOE ?IAIOE

1. O ?acoeueoao? ii?aoethaaiiy aeinooiii? iai e?oa?aoo?e anoaiiaeaii, ui
a?aeii? iaoiaee ciaoiaeaeaiiy onoaeaiiai ia??iaee/iiai noaio
eaac?noaoe?iia?iiai aeaeo?iiaai?oiiai iiey a nooe?eueiiio na?aaeiaeu?
aeathoue ciiao eeoa ciaeoe i?inoi?iaee ?iciiae?e aeaeo?iiaai?oiiai iiey
o o?eniaaiee iiiaio /ano. Aeey oiai, uia ciaeoe i?inoi?iai-/aniaee
?iciiae?e aeaeo?iiaai?oiiai iiey, iaiao?aeia aaaaoi?aciaa ?ica’ycaiiy
caaea/? a?ae ii/aoeo aei e?ioey.

2. O ?acoeueoao? aeeiiaieo o ?iaio? aeine?aeaeaiue iieacaii, ui o?eueee
a ?acoeueoao? ?ica’ycaiiy aeaioi/eiai? t-ia??iaee/ii? (ca /anii)
e?aeiai? caaea/? aeey iae?i?eieo aeaoa?aioe?aeueieo ??aiyiue
eaac?noaoe?iia?iiai aeaeo?iiaai?oiiai iiey iaea?aeo?ii iiaiee
i?inoi?iai-/aniaee ?iciiae?e iiey ia ia??iae?, i?e/iio ?acoeueoao
iaea?aeo?ii c caaeaiith oi/i?noth, aa?aioiaaiith ?oa?aoe?eieie
oi?ioeaie.

3. O ?acoeueoao? aeeiiaieo a ?iaio? aeine?aeaeaiue canoiniaaii iaoiaee
?ica’ycaiiy aeaioi/eiaeo e?aeiaeo caaea/ aeey cae/aeieo iae?i?eieo
aeeoa?aioe?aeueieo ??aiyiue aei iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue c
/anoeiieie iio?aeieie, ci?oaieo iae?i?ei?eo aeeoa?aioe?aeueieo ??aiyiue
?c cae/aeieie e /anoeiieie iio?aeieie e aei nenoai iae?i?eieo
noaoe?iia?ieo ? ianoaoe?iia?ieo aeeoa?aioe?aeueieo ??aiyiue.

4. *aniao aeene?aoecaoe?th ??aiyiue eaac?noaoe?iia?iiai
aeaeo?iiaai?oiiai iiey o aeiaaeeo iaeii??aeiiai na?aaeiaeua aeioe?eueii
cae?enithaaoe ca yaiei i?eioeeiii, o aeiaaeeo eoneiai-iaeii??aeiiai — ca
iayaiei. Aea?? oiai /e ?ioiai iaoiaeo aeeeoo?oueny aei?noe?noth
i?inoi?iai aeene?aoeciaaieo ??aiyiue, yea, a naith /a?ao, caeaaeeoue
a?ae ?iceeaeo ia?aiao??a na?aaeiaeu eoneiai-iaeii??aeieo cii. Ia??aeei
aeiaiaeeoueny caa?oaoeny aei iayaieo i?eioeei?a o aeiaaeeao aeaio- ?
o?eaei??ieo caaea/ iaeii??aeieo na?aaeiaeu i?e cia/ieo iae?i?eiinoyo ? c
?inoii /anoioe aeioooth/eo neaiae?a.

5. Iaoiae ?ica’ycaiiy aeaioi/eiaeo e?aeiaeo caaea/ ia i?aenoaa?
iiaoaeiae iao?eoeue /ooeeainoae aei ii/aoeiaeo oiia ?
iaeoi?aa?naeuei?oee c on?o a?aeiieo, ine?eueee a?i aea? iiaeeea?noue
iiaoaeiae ?aeeieo aeai?eoi?a aiae?co o?ce/ieo nenoai aoe?eiio — aeey
?ic?aooieo ia??iaee/ieo ? onoaeaieo i?ioean?a, aecia/aiiy noaoe/ii?
no?eeino? ia??iaee/ieo ?ica’yce?a, a oaeiae ?ic?aooieo ia?aiao?e/ieo
/ooeeainoae.

6. ?ica’ycaiiy aeaioi/eiaeo t-ia??iaee/ieo i?inoi?iaeo caaea/
aeaeo?iaeeiai?ee ca iaoiaeii iiaoaeiae iiaeaeae /ooeeaino? aei
ii/aoeiaeo oiia ?c-ca neeaaeiino? iaiaaeaia aeiaaeeii ii??aiyii
ianeeaaeieo caaea/.

7. Iniiaiei iaoiaeii ?ica’ycaiiy t-ia??iaee/ieo aeai- ? o?eaei??ieo
i?inoi?iaeo caaea/ aeaeo?iaeeiai?ee ? iaoiae ei?aeoe?? ca na?aaei?ie
cia/aiiyie, yeui aeio?eiai? eiai oiiae canoinoaaiiy . Ia?aaaaith oeueiai
iaoiaeo ? oa, ui ooo a?aeiaaeathoue iio?aae ?ioaa?oaaiiy aeiaeaoeiaeo
aa??aoe?eieo ??aiyiue ? ia/eneaiiy iao?eoe? sseia? aeo?aeieo ??aiyiue.

8. I?ia?aiia ?aae?caoe?y iaoiae?a iiaoaeiae iiaeaeae /ooeeaino? aei
ii/aoeiaeo oiia ? ei?aeoe?? ca na?aaei?ie cia/aiiyie ?ica’ycaiiy
aeaioi/eiaeo t-ia??iaee/ieo i?inoi?iaeo caaea/ aeaeo?iaeeiai?ee
i?aeoaa?aeeea iaae?ei?noue, aenieo aoaeoeai?noue ? ia?niaeoeai?noue ?o
canoinoaaiiy a i?inoi?iaeo caaea/ao i?aaeiaoieo iaeanoae canoinoaaiiy.

9. ?ic?iaeai? a ?iaio? iaoiaee ?ica’ycaiiy t-ia??iaee/ieo aeaioi/eiaeo
e?aeiaeo caaea/ aeaeo?iaeeiai?ee i?eaeaoi? aei ?ica’ycaiiy aoaeue-yeeo
nenoai ci?oaieo e?i?eieo ? iae?i?eieo aeeoa?aioe?aeueieo ??aiyiue, ui
iienothoue o?ce/iee i?ioean ?ioi? i?e?iaee — iaoai?/iee, oaieiaee,
aeeooc?eiee oiui.

Nienie ioaeIeaoeIe ca oaiith aeena?oaoeI?Nienie ioaeIeaoeIe ca oaiith
aeena?oaoeI?

1. *aaai A.A. I?enei?aiee iiooe noaoeiiia?ieo i?ioeania a iaeiiaeii?ieo
i?inoi?iaeo caaea/ao aeaeo?iaeeiaiiee// A?niee AeO «Euea?anueea
iie?oaoi?ea» Aeaeo?iaia?aaoe/i? oa aeaeo?iiaoai?/i? nenoaie». — 1991. —
Aei. 253. — N. 99-102.

2. *aaai A.A., Eia?a/ae ss.A., Aeue ?aaaaaa A.A., E?ioiaeueiee A.?.
Ia?aiao?e/ia /ooeea?noue aeeiiaa/iai aneio?iiiiai iioi?a c ianeaiei
oa?iiaaiaoiei ?ioi?ii// A?niee AeO «Euea?anueea iie?oaoi?ea»
Aeaeo?iaia?aaoe/i? oa aeaeo?iiaoai?/i? nenoaie». — 1997. — Aei. 334. —
N. 137-139.

3. ?.Aouae, A.*aaai, I.Ia/ae, I.?aa/oe. Eiii’thoaoeiy aeaeo?iiaaiaoiiai
iiey a ?ooiieo cano?oieaieo coa/anoeo no?oeoo?ao// Oaoii/ii ainoi. —
1998/1 (6), 2 (7). — N. 50-53.

4. A.*aaai, I.Eaeaithe. Eiii’thoaoeiy t-ia?iiaee/iiai ?ica’yceo iaeii??
aeaiaeii?ii? i?inoi?iai? caaea/i aeaeo?iaeeiaiiee// Oaoii/ii ainoi. —
1998/1 (6), 2 (7). — N 73-76.

5. *aaai A.A. O?aaiaiey aneio?iiiiai aeaeaaoaey a iaeiioaciii ?aaeeia//
Yeaeo?iyia?aaoe/aneea nenoaiu. — 1989. — Aei. 234. — N. 110-112.

6. Aieoayoieeia A.O., I?ioeee N.I., *aaai A.A. Oi?iiaaoaeue neaaaeei a
a?oioa// Aaoi?neia naeaeaoaeuenoai NNN?, ? 1530693, 1988, 3 n.

7. Aouae ?., ?aaaaaa I., *aaai A. Eiii’thoa?ia neioethaaiiy
aeaeo?iiaoaii/ieo i?ioeania o oai?i? aeaeo?iiaaiioiiai iiey// Oacenu
aeieeaaeia Oe?aeineie eiioa?aioeee “Iiaeaee?iaaiea e enneaaeiaaiea
onoie/eainoe nenoai“. — Eeaa. — 1996, 20-24 iae. — N. 42.

8. Iaeaoei Ae., ?aaaaaa A., *aaai A. Eiii’thoa?ia neioethaaiiy
eaacinoaoeiiia?iiai iiey aeaeo?ioaoii/ieo i?eno?i?a// Oacenu aeieeaaeia
Oe?aeineie eiioa?aioeee “Iiaeaee?iaaiea e enneaaeiaaiea onoie/eainoe
nenoai“. — Eeaa. — 1996, 20-24 iae. N. 108.

AiioaoeIssAiioaoeIss

*aaai A.A. Iaoaiaoe/ia iiaeaethaaiiy aeaioi/eiaeo t-ia??iaee/ieo
e?aeiaeo caaea/ aeaeo?iaeeiai?ee. — ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe
ca niaoe?aeuei?noth 01.05.02 — iaoaiaoe/ia iiaeaethaaiiy oa
ia/enethaaeuei? iaoiaee. — Aea?aeaaiee oi?aa?neoao «Euea?anueea
iie?oaoi?ea», Euea?a, 1999.

Caoeua?oueny 8 iaoeiaeo i?aoeue, ye? i?enay/ai? ?ic?aooieo onoaeaieo
o?ce/ieo iie?a, ui iienothoueny ci?oaieie iae?i?eieie
aeeoa?aioe?aeueieie ??aiyiiyie c /anoeiieie e cae/aeieie iio?aeieie.
Iaoiaee aiae?co a?oioothoueny ia ?ica’ycaii? aeaioi/eiaeo t-ia??iaee/ieo
e?aeiaeo caaea/. O ?acoeueoao? ?oa?aoe?eieo oeeee?a ia/eneththoueny oae?
ii/aoeia? oiiae, ui aeeeth/athoue ia?ao?aeio ?aaeoe?th e aeathoue ciiao
aa?eoe aaciina?aaeiuei a onoaeaiee ia??iaee/iee i?ioean. I?inoi?iaa
aeene?aoecaoe?y aeo?aeieo ??aiyiue cae?enith?oueny ca iaoiaeaie
ne?i/aiieo ??cieoeue aai ne?i/aiieo aeaiaio?a, /aniaa aeene?aoecaoe?y —
ca yaiei aai iayaiei iaoiaeaie. ?ica’ycothoueny iaeii- e aeaiaei??i?
i?inoi?ia? caaea/? eaac?noaoe?iia?iiai aeaeo?iiaai?oiiai iiey a
nooe?eueieo ? eoneiai-iaeii??aeieo iae?i?eieo na?aaeiaeuao.

Eeth/ia? neiaa: aeaioi/eia? e?aeia? caaea/?, iae?i?ei? aeeoa?aioe?aeuei?
??aiyiiy c /anoeiieie e cae/aeieie iio?aeieie, i?inoi?ia? caaea/?
aeaeo?iaeeiai?ee.

AiiioaoeessAiiioaoeess

*aaai A.A. Iaoaiaoe/aneia iiaeaee?iaaiea aeaoooi/a/iuo t-ia?eiaee/aneeo
e?aaauo caaea/ yeaeo?iaeeiaieee. — ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 01.05.02 — iaoaiaoe/aneia iiaeaee?iaaiea e
au/eneeoaeueiua iaoiaeu. — Ainoaea?noaaiiue oieaa?neoao «Eueaianeay
iieeoaoieea», Eueaia, 1999.

Caueuaaony 8 iao/iuo o?oaeia, iinayuaiuo ?an/aoo onoaiiaeaoeony
oece/aneeo iieae, eioi?ua iienuaathony niaoaiuie iaeeiaeiuie
aeeooa?aioeeaeueiuie o?aaiaieyie n /anoiuie e iaueiiaaiiuie
i?iecaiaeiuie. Iaoiaeu aiaeeca aace?othony ia ?aoaiee aeaoooi/a/iuo
t-ia?eiaee/aneeo e?aaauo caaea/. A ?acoeueoaoa eoa?aoeeiiiuo oeeeeia
au/eneythony oaeea ia/aeueiua oneiaey, eioi?ua eneeth/atho ia?aoiaeioth
?aaeoeeth e aeatho aiciiaeiinoue aieoe iaiin?aaenoaaiii a onoaiiaeaoeeny
ia?eiaee/aneee i?ioean. I?ino?ainoaaiiay aeene?aoecaoeey enoiaeiuo
o?aaiaiee inouanoaeyaony iaoiaeaie eiia/iuo ?aciinoae eeai eiia/iuo
yeaiaioia, a?aiaiiay aeene?aoecaoeey — yaiui eeai iayaiui iaoiaeaie.
?aoathony iaeii- e aeaooia?iua i?ino?ainoaaiiua caaea/e yeaeo?iaeeiaieee
a nieioiuo e eoni/ii-iaeii?iaeiuo iaeeiaeiuo n?aaeao.

Eeth/aaua neiaa: aeaoooi/a/iua e?aaaua caaea/e, iaeeiaeiua
aeeooa?aioeeaeueiua o?aaiaiey n /anoiuie e iaueiiaaiiuie i?iecaiaeiuie,
i?ino?ainoaaiiua caaea/e yeaeo?iaeeiaieee.

AbstractAbstract

Tchaban A.V. Mathematical modelling of two point t-periodical value
problem of electrodynamics.- Manuscript.

Thesis for a candidate’s degree by speciality 01.05.02- mathematical
modelling and computing methods. — State University «Lviv polytechnic»,
Lviv, 1999.

The dissertation is devoted to the calculation of steady-state physical
fields, which circumscribed by mixed nonlinear differential equations
with partial and ordinary derivatives. The methods of analysis are based
on the two-point t-periodical boundary problems. As a result of
integration cycles boundary conditions which exclude transient reaction
and give opportunity to enter directly into steady-state periodical
process are calculated. The spatial discretization of starting equations
is done by finite difference method or finite elements method, the time
discretization — by explicit or implicit me-

thods. The spatial one- and two-dimensional problems of electrodynamics
in continuous and piece-homogeneous nonlinear media are solved.

Such approach firstly give opportunity to obtain spatial-time
distribution of sought functions on time period by one execution of a
program. The known methods make it possible to obtain spatial
distribution of such functions in the fixed moment of time only, and for
obtaining spatial-time distribution it is necessary to solve the problem
for the series of discrete means functions of time once more.

The two basic methods of boundary value problems solving are proposed in
the work — the method of construction of models of sensitivities to the
initial conditions and the method of correction by the intermediate
mean. The first one is universal and can be used formally to any
spatial-time boundary problems, but it is comparatively difficult in
program realization. The second one is very simple but it is limited by
the sought functions which have not constant components and if have it,
then they must be known before. So the first method is proposed now for
the system with correspondingly low order, and the second method may be
used directly to the systems with high order, and for present time it is
the single method which can solve such problems.

The both methods are the Cauchy problem for integration of nonlinear
differential equations of state from given initial conditions, so the
algorithm of calculation though they are intended for analysis of
steady-state processes, but in advance they spread to the analysis of
transient processes. Transient process we obtain as a result of
integration of differential equations from any initial conditions, and
steady-state one — from initial conditions, which except transient
reaction. So, such initial conditions must be calculated as a result of
transcendental equations solving of time periodicity, which are imposed
on differential equations of state (target equations).

In the method which is based on the solving of matrix of sensitivities
to the initial conditions the equations of periodicity are solved by
Newton’s method of iterations. The Jakobi matrix is found from the
matrix of monodromy, which is calculated as a result of nonlinear
differential equations of state and linear differential equation of
first variation integration on the time interval which is equal one
period.

The method of correction by the intermediate means of unknowns on the
time period not needs integration of the additional variational
equations. The iterative process is built by the maximal and minimal
means of functions on the time period and it’s means at the end of
period which is obtained as a result of integration of equations of
state on the period.

The resources of the proposed methods of solving t-periodical boundary
problems of electrodynamics are illustrated by the next examples:

— one-dimensional spatial boundary problem for nonlinear differential
equations with partial derivatives of calculation of steady-state
process in the thin steel sheet;

— one-dimensional spatial boundary problem for nonlinear differential
equations with partial derivatives of calculation of steady-state
process in laminated ferromagnetic toroid, moreover, the laminated
structure is equivalently by continuous anisotropic medium;

— one-dimensional spatial boundary problem for nonlinear mixed
differential equations with partial and ordinary derivatives of
calculation of steady-state process in toroidal choke;

— two-dimensional spatial boundary problem for nonlinear differential
equations with partial derivatives of calculation of steady-state
process in solid ferromagnetic toroid;

— two-dimensional spatial boundary problem for nonlinear
algebraic-differential equations with partial derivatives of calculation
of steady-state process in laminated ferromagnetic toroid, moreover, the
laminated structure is considered as real piece-homogeneous structure as
alternate ferromagnetic and air gaps.

All the presented methods have a good numerical stability of
computation.

Key words: two-points boundary problems, nonlinear differential
equations with partial and ordinary derivatives, spatial electrodynamics
problems.

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