.

Метод усереднення в крайових задачах для диференціальних рівнянь з відхиленим аргументом: Автореф. дис… канд. фіз.-мат. наук / М.П. Філіпчук, Чернів

Язык: украинский
Формат: реферат
Тип документа: Word Doc
138 2304
Скачать документ

*A?I?AAOeUeEEE AeA?AEAAIEE OI?AA?NEOAO

?I. TH.OAAeUeEIAE*A

O ? e ? i / o e I e e i e a I a o ? i a e /

OAeE 517.929.7

IAOIAe ONA?AAeIAIIss A E?AEIAEO CAAeA*AO AeEss AeEOA?AIOe?AEUeIEO
??AIssIUe C A?AeOEEAIEI A?AOIAIOII

01.01.02 – aeeoa?aioe?aeuei? ??aiyiiy

Aaoi?aoa?ao

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

*a?i?aoe? – 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia ia eaoaae?? i?eeeaaeii? iaoaiaoeee ?
iaoai?ee

*a?i?aaoeueeiai aea?aeaaiiai oi?aa?neoaoo ?i. TH.Oaaeueeiae/a

Iaoeiaee ea??aiee :

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe,
aeioeaio

A?AOI ss?ineaa Eineiiae/,

*a?i?aaoeueeee aea?aeaaiee
oi?aa?neoao ?i. TH.Oaaeueeiae/a,

eaoaae?a i?eeeaaeii? iaoaiaoeee ?
iaoai?ee

Io?oe?ei? iiiiaioe :

aeieoi? o?ceei-iaoaiaoe/ieo iaoe,
i?ioani?

AIE*OE Ieaenaiae? Aiae??eiae/,

?inoeooo iaoaiaoeee IAI Oe?a?ie,

a?aeae?e cae/aeieo
aeeoa?aioe?aeueieo ??aiyiue,

i?ia?aeiee iaoeiaee ni?a?ia?oiee

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe,
aeioeaio

EEAA*OE ?aai ?aaiiae/,

*a?i?aaoeueeee aea?aeaaiee
oi?aa?neoao ?i. TH.Oaaeueeiae/a,

eaoaae?a iaoaiaoe/iiai iiaeaethaaiiy

I?ia?aeia onoaiiaa :

Iaeanueeee aea?aeaaiee oi?aa?neoao
?i. ?.?. Ia/ieeiaa,

eaoaae?a aeiiii?/ii? e?aa?iaoeee
? iioeiaeueiiai

ea?oaaiiy,

i. Iaeana

Caoeno a?aeaoaeaoueny 11 /a?aiy 1999 ?. i 14 aiaeei?

ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee E 76.051.02

a *a?i?aaoeueeiio aea?aeaaiiio oi?aa?neoao? ?i. TH.Oaaeueeiae/a

ca aae?anith: 274012, i. *a?i?aoe?, aoe. Oi?aa?neoaonueea, 28 (ei?ion 1)

C aeena?oaoe??th iiaeia iciaeiieoeny o iaoeia?e a?ae?ioaoe?

*a?i?aaoeueeiai aea?aeaaiiai oi?aa?neoaoo ?i. TH.Oaaeueeiae/a

( 274000, i. *a?i?aoe?, aoe. Ean? Oe?a?iee, 23)

Aaoi?aoa?ao ?ic?neaiee 7 o?aaiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee
Naaeia’ye A.I.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Aeeoa?aioe?aeuei? ??aiyiiy c a?aeoeeaiei a?aoiaioii
ciaoiaeyoue oe?iea canoinoaaiiy a oai??? aaoiiaoe/iiai ?aaoethaaiiy,
oaeaiaoai?oe?, ?aae?ieieaoe??, aeaeo?i- ? ?aae?ioaoi?oe?,
aeine?aeaeaiiyo c ?aeaoii? oaoi?ee, oa?iiyaea?iiai neioaco,
ei?aaeaaoaeoaaiiy, iaaeeoeeie, a?ieia???, aeieia??, aeiaaino?ieiaiai
i?iaiicoaaiiy a aeiiii?oe? oa aaaaoueio ?ioeo aaeocyo iaoee ? oaoi?ee.

Ii/eiath/e ?c na?aaeeie 40-o ?ie?a XX noie?ooy, caieoe aeuacaaaeaieo
i?eeeaaeieo iaoe iaoiiaeee ?ioaineaiee ?icaeoie oai???
aeeoa?aioe?aeueieo ??aiyiue c a?aeoeeaiei a?aoiaioii. Ia aeaiee /an
??ci? ?? aniaeoe aena?oeaii o ooiaeaiaioaeueieo iiiia?ao?yo
E.A.Aeuenaieueoea ? N.A.Ii?e?ia; N.A.Ii?e?ia; A.Ae.Ieoe?na; ?.Aaeeiaia ?
E.E.Eoea; A.I?ii?; A.I.?oaaieea; Aeae.Oaeea; TH.I.Ieo?iiieuenueeiai ?
Ae.?.Ia?oeithea; TH.I.Ieo?iiieuenueeiai, A.I.Naiieeaiea ?
Ae.?.Ia?oeithea; A.A.Eieiaiianueeiai ? A.?.Iiniaa; ?.O.Oea?ueeiaa;
I.A.Acaae?aa, A.I.Iaeneiiaa ? E.O.?aoiaooee?ii?; I.A.Aie/oea,
A.O.AEo?aaeueiaa ? A.I.Naiieeaiea oa ?i.

Iaeia ?c /?eueieo i?noeue a oai??? aeeoa?aioe?aeueieo ??aiyiue
caeiathoue i?iaeaie aeine?aeaeaiiy ?nioaaiiy ? iiaoaeiae aeai?eoi?a
ciaoiaeaeaiiy ?ica’yce?a e?aeiaeo caaea/. ?ic?iaea eiino?oeoeaieo
iaoiae?a, ye? a aeicaieyee aoaeoeaii ?ica’ycoaaoe oe? i?iaeaie aeey
aeineoue oe?ieeo eean?a caaea/, caeeoa?oueny iaeiei ?c i??i?eoaoieo
iai?yi?a ?icaeoeo oai??? aeeoa?aioe?aeueieo ??aiyiue. Iineeaia oaaaa aei
oai??? e?aeiaeo caaea/ iaoiiaeaia oaeiae ? oei, ui aiia ioiieth? oaeee
aaaeeeaee ?icae?e oai??? aeeoa?aioe?aeueieo ??aiyiue, ye oai??y
ia??iaee/ieo ?ica’yce?a.

O aeiaaeeo cae/aeieo aeeoa?aioe?aeueieo ??aiyiue oai??y e?aeiaeo caaea/
aieiae?? aeineoue iiooaeiei a?naiaeii ??ciiiai?oieo iaoiae?a. Oiio
i?e?iaeiei /eiii iinoa? ieoaiiy i?i canoinoaaiiy oeeo iaoiae?a aei
aeeoa?aioe?aeueieo ??aiyiue c a?aeoeeaiei a?aoiaioii. Iniaeeai
aaaeeeaiai oai?aoe/iiai oa i?aeoe/iiai cia/aiiy, ia iao iiaeyae, iaaoaa?
canoinoaaiiy oaeiai aoaeoeaiiai iaoiaeo, ye iaoiae ona?aaeiaiiy. O
aeiaaeeo cae/aeieo aeeoa?aioe?aeueieo ??aiyiue e?aeia? caaea/? iei
aoaeoeaii aeine?aeaeoaaee o ni?eueieo ?iaioao Ae.Ae.Aaeiia,
I.I.Eiinoaio?iia, N.Ae.I?eooaaa, TH.I.Ieo?iiieuenueeee, a oaeiae
E.Ae.Aeoeaiei; A.I.Ieioi?eia ? O.N.Ca??eiaa; A.I.Ieioi?eia ?
A.A.Aa?aeae. O aeiaaeeo ae e?aeiaeo caaea/ aeey aeeoa?aioe?aeueieo
??aiyiue c a?aeoeeaiei a?aoiaioii iaoiae ona?aaeiaiiy iiee-ui ia ciaeoia
iaeaaeiiai canoinoaaiiy. A?aecia/eii o oeueiio iai?yieo ?acoeueoaoe,
io?eiai? Ae.Ae.Aaeiiaei ? N.Ae.I?eooaaith; TH.I.Ieo?iiieuenueeei,
Ae.Ae.Aaeiiaei ? N.Ae.I?eooaaith; A.I.AEieo?eiaei ? A.A.Aoaiae??aei .

. Cia/ia oaaaa aei ieo iaoiiaeaia iacanoiniai?noth aeia?a a?aeiiiai
iaoiaeo ?ica’ycaiiy ii/aoeiaeo oa aeayeeo e?aeiaeo caaea/ – iaoiaeo
e?ie?a.

O iaoiae? ona?aaeiaiiy, aeeeaaeaiiio a ?iaio?, iaeiei ?c aieiaieo
i?eiouaiue aoaea ?nioaaiiy oa a?aeiiee aiae?oe/iee aeaeyae ?ica’yce?a
a?aeiia?aeieo ona?aaeiaieo nenoai. O aeiaaeeo nenoai aeeoa?aioe?aeueieo
??aiyiue c a?aeoeeaiei a?aoiaioii, a yeeo cai?ciaiiy ia ? iaiaaeaiei,
eiai iio??aii caa??aaoe ? a ona?aaeiaieo nenoaiao. Oiio aeieea? i?iaeaia
aeine?aeaeaiiy ona?aaeiaieo e?aeiaeo caaea/. O aeayeeo /anoeiaeo
aeiaaeeao, iai?eeeaae,

,

i?eoiaeeii aei nenoaie

.

A e?aeia? caaea/? aeey ia? iiaeia aoaeoeaii aeine?aeaeoaaoe ca
aeiiiiiaith aeeeaaeaiiai o iaeiiio ?c ?icae?e?a /enaeueii-aiae?oe/iiai
iaoiaeo. I?e oeueiio ioiieaii iaa?oue cia/ii oe?oee eean nenoai.

Caoaaaeeii oaeiae, ui aeey cae/aeieo aeeoa?aioe?aeueieo ??aiyiue
/enaeueii-aiae?oe/iee iaoiae ?icaeiooee o ?iaioao A.I.Naiieeaiea ?
I.E.?iioi; I.E.?iioi ? O.A.Naa?ii?; A.I.Naiieeaiea ? N.A.Ia?oeithea;
?.I.O?ioei/oea ? I.A.Eiaaeaiea, a eiai iioe?aiiy ia aeeoa?aioe?aeuei?
??aiyiiy c a?aeoeeaiei a?aoiaioii ? aeineoue aeooaeueiith i?iaeaiith.
?acoeueoaoe a oeueiio iai?yieo io?eiaee Ae.?.Ia?oeithe ? A.I.Naiieeaiei;
TH.I.Ieo?iiieuenueeee, A.I.Naiieeaiei ? Ae.?.Ia?oeithe; A.Aaaonoeiia?/ ?
I.Eaai?o; I.Eaai?o oa N.A.ssi/oe .

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. ?iaioa aeeiiaia
a ?aieao oaie «sse?ni? ? iaaeeaeai? iaoiaee aeine?aeaeaiiy
aeeoa?aioe?aeueieo oa aeeoa?aioe?aeueii-ooieoe?iiaeueieo ??aiyiue ? ?o
canoinoaaiiy», ui aeeiio?oueny ia eaoaae?? i?eeeaaeii? iaoaiaoeee ?
iaoai?ee *a?i?aaoeueeiai aea?aeaaiiai oi?aa?neoaoo ?i.TH.Oaaeueeiae/a
ca?aeii c Eii?aeeiaoe?eiei ieaiii iaoeiaeo aeine?aeaeaiue I?i?noa?noaa
Ina?oe Oe?a?ie c iai?yieo «Aaiiao?e/i? oa aiae?oe/i? iaoiaee a
iaoaiaoeoe? ? ?o canoinoaaiiy».

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith aeaii? ?iaioe ? no?iaa iaoaiaoe/ia
iaa?oiooaaiiy canoiniaiino? iaoiaeo ona?aaeiaiiy oa
/enaeueii-aiae?oe/iiai iaoiaeo aei aeine?aeaeaiiy ?ica’yciino? e?aeiaeo
caaea/ aeey aeayeeo eean?a nenoai aeeoa?aioe?aeueieo ??aiyiue c
a?aeoeeaiei a?aoiaioii.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. Iaoeiao iiaecio ?iaioe
aecia/athoue ianooii? iniiai? ?acoeueoaoe:

iaa?oioiaaii iaoiae ona?aaeiaiiy a ii/aoeiaeo caaea/ao aeey aeayeeo
iiaeo eean?a nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ci?iiei cai?ciaiiyi,
a aeey ??cieoe? ?ica’yce?a aeo?aeieo ? ona?aaeiaieo nenoai ia
aneiioioe/ii aaeeeiio ?ioa?aae? /ano anoaiiaeaii yaii caeaaeio a?ae
iaeiai ia?aiao?a ioe?ieo /anoeiii? iio?aeii? ii ii/aoeiaiio cia/aiith;

ca aeiiiiiaith iaoiaeo ona?aaeiaiiy aeine?aeaeaii ?ica’yci?noue e?aeiaeo
caaea/ aeey aeayeeo eean?a nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ci?iiei
cai?ciaiiyi;

?icaeiooi /enaeueii-aiae?oe/iee iaoiae aeine?aeaeaiiy aeaioi/eiaeo
e?aeiaeo caaea/ aeey nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ia?aoai?aiei
a?aoiaioii;

aia?oa iaa?oioiaaii /enaeueii-aiae?oe/iee iaoiae aeine?aeaeaiiy e?aeiaeo
caaea/ aeey nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ia?aoai?aiei
a?aoiaioii o aeiaaeeo aaaaoioi/eiaeo ? ?ioaa?aeueieo e?aeiaeo oiia.

Aeinoia??i?noue io?eiaieo ?acoeueoao?a caaacia/o?oueny iayai?noth
no?iaeo iaoaiaoe/ieo aeiaaaeaiue.

I?aeoe/ia cia/aiiy iaea?aeaieo ?acoeueoao?a. Aeena?oaoe?y ia?, a
iniiaiiio, oai?aoe/iee oa?aeoa?. ?ic?iaeai? o i?e iaoiaee aeine?aeaeaiiy
iiaeooue aooe ia?aianai? ia aiaeia?/i? eeane aeeoa?aioe?aeueieo ??aiyiue
c a?aeoeeaiei a?aoiaioii a?eueo caaaeueiiai aeaeyaeo. E??i oeueiai,
io?eiai? ?acoeueoaoe iiaeooue aooe aeei?enoai? i?e ?ica’ycoaaii?
eiie?aoieo i?eeeaaeieo caaea/.

Iniaenoee aianie caeiaoaa/a. O aeena?oaoe?? oa aeaio ni?eueieo
ioae?eaoe?yo iaoeiaiio ea??aieeo – A?aoio ss.E. – iaeaaeaoue iinoaiiaee
caaea/ oa aecia/aiiy caaaeueii? noaie aeine?aeaeaiiy, a aeiaaaeaiiy an?o
iaaaaeaieo oaa?aeaeaiue – iniaenoi aeena?oaioo. Iaoiaeeea aeine?aeaeaiiy
e?aeiaeo caaea/ ca aeiiiiiaith iaoiaeo ona?aaeiaiiy caiice/aia ?c ?ia?o
?.?.Iao?eoeia; A.I.Naiieeaiea ? ss.?.Iao?eoeia; TH.I.Ieo?iiieuenueeiai,
Ae.Ae.Aaeiiaa ? N.Ae.I?eooaai?, a ca aeiiiiiaith /enaeueii-aiae?oe/iiai
iaoiaeo – ?c ?ia?o A.I.Naiieeaiea ? I.E.?iioi.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe ?iaioe
aeiiia?aeaeeny ? iaaiai?thaaeeny ia Anaoe?a?inuee?e eiioa?aioe??
«Aeeoa?aioe?aeueii-ooieoe?iiaeuei? ??aiyiiy oa ?o canoinoaaiiy»
(*a?i?aoe?, 1996), Anaoe?a?inuee?e oeie?-nai?ia?? «Iae?i?ei? e?aeia?
caaea/? iaoaiaoe/ii? o?ceee oa ?o canoinoaaiiy»
(Eai’yiaoeue-Iiae?euenueeee, 1997), I?aeia?iaei?e eiioa?aioe??
«Iiaeaethaaiiy ? aeine?aeaeaiiy no?eeino? nenoai» (Ee?a, 1997), Nueii?e
I?aeia?iaei?e iaoeia?e eiioa?aioe?? ?iai? aeaaeai?ea I.E?aa/oea (Ee?a,
1998), I?aeia?iaei?e iaoeia?e eiioa?aioe?? «No/ani? i?iaeaie iaoaiaoeee»
(*a?i?aoe?, 1998), iaoeiaeo nai?ia?ao iaoaiaoe/iiai oaeoeueoaoo oa
eaoaae?e i?eeeaaeii? iaoaiaoeee ? iaoai?ee *a?i?aaoeueeiai aea?aeaaiiai
oi?aa?neoaoo ?i. TH.Oaaeueeiae/a.

Ioae?eaoe??. Ca ?acoeueoaoaie aeine?aeaeaiue, cae?eniaieo o
aeena?oaoe??, iioae?eiaaii 9 i?aoeue : 2 noaoo? o iaoeiaeo
aeo?iaeao, 3 noaoo? o ca??ieeao iaoeiaeo i?aoeue ?inoeoooo iaoaiaoeee
IAI Oe?a?ie, 2 noaoo? o iaoa??aeao i?aeia?iaeieo iaoeiaeo eiioa?aioe?e
oa 2 oac o aeiiia?aeyo iaoeiaeo eiioa?aioe?e.

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny ?c anooio,
/ioe?ueio ?icae?e?a, ?icaeoeo ia 16 i?ae?icae?e?a, aeniiae?a oa nieneo
aeei?enoaieo aeaea?ae ?c 86 iaeiaioaaiue. Caaaeueiee ianya aeena?oaoe??
– 142 noi??iee iaoeiiieniiai oaenoo.

INIIAIEE CI?NO ?IAIOE

O ia?oiio ?icae?e? i?iaiae?ciaaii ?icaeoie oa canoinoaaiiy aei
aeeoa?aioe?aeueieo ??aiyiue c a?aeoeeaiei a?aoiaioii iaoiaeo
ona?aaeiaiiy ? /enaeueii-aiae?oe/iiai iaoiaeo, a oaeiae ei?ioei
aeeeaaeaii iniiaiee ci?no ?iaioe.

O ae?oaiio ?icae?e? ca aeiiiiiaith iaoiaeo ona?aaeiaiiy
aeine?aeaeothoueny e?aeia? caaea/? aeey nenoaie aeeoa?aioe?aeueieo
??aiyiue ?c ci?iiei cai?ciaiiyi aeaeyaeo

,
(1)

.

Ii?yae ?c (1) ?icaeyaea?oueny a?aeiia?aeia ona?aaeiaia nenoaia

,
(2)

aea

.

Caoaaaeeii, ui nenoaia (2) cia/ii i?ino?oa a?ae aeo?aeii? nenoaie (1).

.

anoaiiaeai? a?aeiia?aeii ioe?iee

,

.

O i?ae?icae?e? 2.2 aeey nenoaie (1) ?icaeyaeathoueny iae?i?ei?
aeaioi/eia? e?aeia? oiiae aeaeyaeo

,
(3)

-aei??ia aaeoi?-ooieoe?y.

Aeinoaoi? oiiae ?ica’yciino? e?aeiai? caaea/? (1), (3) aeacai? o oai?ai?
2.2.1.

Oai?aia 2.2.1. Iaoae aeeiiothoueny oiiae:

;

ona?aaeiaia e?aeiaa caaea/a (2), (4)

(4)

, yeee eaaeeoue ?acii

;

;

4) iao?eoey

,

, ?

;

oaea, ui

.

.

O oai?ai? 2.2.2 aiaeia?/ia oaa?aeaeaiiy iaaaaeaia o aeiaaeeo iae?i?eieo
aaaaoioi/eiaeo e?aeiaeo oiia aeey nenoaie (1), a o oai?ai? 2.3.1
i?ae?icae?eo 2.3 – o aeiaaeeo ?ioaa?aeueieo e?aeiaeo oiia aeaeyaeo

,

-aei??iee aaeoi?.

aeaeyaeo

),

oa

),

– caaeaia cia/aiiy.

-ieieao ?aeeieo ?ica’yce?a a?aeiia?aeieo ona?aaeiaieo e?aeiaeo caaea/.

O i?ae?icae?e? 2.5 nenoaia (1) ?icaeyaea?oueny aac i?eiouaiiy
ia??iaee/iino? i?aai? /anoeie. Iacaaii oaeo nenoaio iaia??iaee/iith ?
caaeaii aeey ia? e?i?ei? aaaaoioi/eia? e?aeia? oiiae aeaeyaeo

,
(5)

-aei??iee aaeoi?,

Iaoae ?nio? a?aieoey

.
(6)

Oiae? iieeaaeaii o a?aeiia?aei?noue e?aeia?e caaea/? (1), (5)
ona?aaeiaio e?aeiao caaea/o

,

.
(7)

?ica’yce?a e?aeiaeo caaea/ (1), (5) ? (7).

Oai?aia 2.5.1. Iaoae aeeiiothoueny oiiae:

;

?nio? na?aaei? cia/aiiy (6);

;

– noaea iaae?iaeaeaia iao?eoey;

.

a??ia ioe?iea

.

O o?aoueiio ?icae?e? ca aeiiiiiaith iaoiaeo ona?aaeiaiiy
aeine?aeaeothoueny e?aeia? caaea/? aeey nenoaie aeeoa?aioe?aeueieo
??aiyiue ?c ci?iiei iaiaaeaiei cai?ciaiiyi aeaeyaeo

,
(8)

.

Ii?yae ?c (8) ?icaeyaea?oueny a?aeiia?aeia ona?aaeiaia nenoaia

,
(9)

aea

.

.

anoaiiaeai? a?aeiia?aeii ioe?iee

,

.

O i?ae?icae?e? 3.2 aeey nenoaie (8) ?icaeyaeathoueny iae?i?ei?
aeaioi/eia? e?aeia? oiiae aeaeyaeo

,
(10)

-aei??ia aaeoi?-ooieoe?y.

Aeinoaoi? oiiae ?ica’yciino? e?aeiai? caaea/? (8), (10) aeacai? o
oai?ai? 3.2.1.

Oai?aia 3.2.1. Iaoae aeeiiothoueny oiiae:

;

ona?aaeiaia e?aeiaa caaea/a (9), (11)

(11)

, yeee eaaeeoue ?acii c

;

;

4) iao?eoey

,

, ?

;

oaea, ui

.

.

O oai?ai? 3.2.2 aiaeia?/ia oaa?aeaeaiiy iaaaaeaia o aeiaaeeo iae?i?eieo
aaaaoioi/eiaeo e?aeiaeo oiia aeey nenoaie (8), a o oai?ai? 3.3.1
i?ae?icae?eo 3.3 – o aeiaaeeo ?ioaa?aeueieo e?aeiaeo oiia aeaeyaeo

,

-aei??iee aaeoi?.

aeaeyaeo

),

oa

),

– caaeaia cia/aiiy.

-ieieao ?aeeieo ?ica’yce?a a?aeiia?aeieo ona?aaeiaieo e?aeiaeo caaea/.

O i?ae?icae?e? 3.5 nenoaia (8) ?icaeyaea?oueny aac i?eiouaiiy
ia??iaee/iino? i?aai? /anoeie. Iacaaii oaeo nenoaio iaia??iaee/iith ?
caaeaii aeey ia? e?i?ei? aaaaoioi/eia? e?aeia? oiiae aeaeyaeo

,
(12)

-aei??iee aaeoi?,

Iaoae ?nio? a?aieoey

.
(13)

Oiae? iieeaaeaii o a?aeiia?aei?noue e?aeia?e caaea/? (8), (12)
ona?aaeiaio e?aeiao caaea/o

,

.
(14)

?ica’yce?a e?aeiaeo caaea/ (8), (12) ? (14).

Oai?aia 3.5.1. Iaoae aeeiiothoueny oiiae:

;

?nio? na?aaei? cia/aiiy (13);

;

– noaea iaae?iaeaeaia iao?eoey;

.

a??ia ioe?iea

.

– aeayea noaea, oi iiaeia aeei?enoiaoaaoe ye noaio ona?aaeiaiiy,
aeeeaaeaio o ae?oaiio ?icae?e?, oae ? noaio ona?aaeiaiiy, aeeeaaeaio o
o?aoueiio ?icae?e?. I?e oeueiio c?o/i?oa aeei?enoiaoaaoe naia inoaiith
noaio, ine?eueee o i?e ona?aaeiaia nenoaia ia i?noeoue cai?ciaiiy.

, ? nenoaia

,

. ?icaeyaeath/e aeey ia?, iai?eeeaae, e?i?ei? aeaioi/eia? e?aeia? oiiae
aeaeyaeo

,

ca?aeii c (2), io?eio?ii ona?aaeiaio e?aeiao caaea/o

,

.

i?eoiaeeii aei e?aeiai? caaea/?

,

,

aoaeoeaia aeine?aeaeaiiy yei? iiaeia cae?enieoe ca aeiiiiiaith
aeeeaaeaiiai o /aoaa?oiio ?icae?e? /enaeueii-aiae?oe/iiai iaoiaeo.

O oeueiio ?icae?e? aea/athoueny e?aeia? caaea/? aeey nenoaie
aeeoa?aioe?aeueieo ??aiyiue ?c ia?aoai?aiei a?aoiaioii aeaeyaeo

,
(15)

?c iaa?ae’?iieie eiiiiiaioaie.

O i?ae?icae?e? 4.1 aeey nenoaie (15) ?icaeyaeathoueny e?i?ei?
aeaioi/eia? e?aeia? oiiae aeaeyaeo

(16)

-aei??iee aaeoi?.

aeeiio?oueny oiiaa

(17)

.

-ieieii, aea

,

.

Iaoae

(18)

ia ia?aaeuo? iaeeieoe?

.
(19)

?icaeyiaii iine?aeiai?noue ooieoe?e

,

(20)

.

.

? ? ?ica`yceii e?aeiai? caaea/?

,

aea

.

a??ia ioe?iea

(21)

aoea ?ica`yceii e?aeiai? caaea/? (15), (16), aeacai? o oai?ai? 4.1.3.

ii/aoeiai? caaea/?

,

aoa iaeii/anii ?ica`yceii e?aeiai? caaea/? (15), (16), iaiao?aeii ?
aeineoue, uia aecia/aeueia ooieoe?y

ia?aoai?thaaeanue a ioeue

.

aeaeyaeo (20) a??ia ioe?iea (21).

-oei

. Oiio aaaaeaii aei ?icaeyaeo iaaeeaeai? aecia/aeuei? ooieoe?th

(22)

oa ??aiyiiy

.

Aeinoaoi? oiiae ?ica`yciino? e?aeiai? caaea/? (15), (16) aeacai?
o oai?ai? 4.1.4.

Oai?aia 4.1.4. Iaoae aeeiiothoueny oiiae oai?aie 4.1.1, a oaeiae oiiae:

iaioeueiaiai ?iaeaeno;

aeeiio?oueny ia??ai?noue

, ii/aoeiaa cia/aiiy yeiai

(23)

.

Iaiao?aei? ae oiiae ?ica’yciino? e?aeiai? caaea/? (15), (16) aeacai? o
oai?ai? 4.1.6.

aeeiioaaeanue ia??ai?noue

,

a?aeiia?aeii.

. Ine?eueee i?e oeueiio aeeeaaeaia o iiia?aaeiueiio ioieo? noaia
/enaeueii-aiae?oe/iiai iaoiaeo ? iacanoiniaiith, o oai?ai? 4.1.7
iaaaaeaii ?? iiaeeo?eaoe?th, aea iaia? iio?aae ?ica’ycoaaoe
aecia/aeueia ??aiyiiy.

Oai?aia 4.1.7. Iaoae aeeiiothoueny oiiae:

iaae?iaeaeaia;

-ieieii,

aa?aoueny iieiiiiiaioii );

iaioa iaeeieoe?.

, yeee ? a?aieoeath iine?aeiaieo iaaeeaeaiue

,

.

?acoeueoaoe, oe?eeii aiaeia?/i? ?acoeueoaoai i?ae?icae?eo 4.1, io?eiai?
aeey nenoaie (15) o i?ae?icae?e? 4.2 o aeiaaeeo e?i?eieo aaaaoioi/eiaeo
e?aeiaeo oiia aeaeyaeo

-aei??iee aaeoi?, a o i?ae?icae?e? 4.3 – o aeiaaeeo ?ioaa?aeueieo
e?aeiaeo oiia aeaeyaeo

,

-aei??iee aaeoi?.

AENIIAEE

Aeena?oaoe?y ia?, a iniiaiiio, oai?aoe/iee oa?aeoa?. Iaaaaeai? o i?e
?acoeueoaoe aeiiiaiththoue a?aeii? aeine?aeaeaiiy e?aeiaeo caaea/ aeey
aeeoa?aioe?aeueieo ??aiyiue c a?aeoeeaiei a?aoiaioii ca aeiiiiiaith
iaoiaeo ona?aaeiaiiy oa /enaeueii-aiae?oe/iiai iaoiaeo. I?e oeueiio
io?eiaii ianooii? iia? iaoeia? ?acoeueoaoe:

iaa?oioiaaii iaoiae ona?aaeiaiiy a ii/aoeiaeo caaea/ao aeey aeayeeo
iiaeo eean?a nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ci?iiei cai?ciaiiyi,
a aeey ??cieoe? ?ica’yce?a aeo?aeieo ? ona?aaeiaieo nenoai ia
aneiioioe/ii aaeeeiio ?ioa?aae? /ano anoaiiaeaii yaii caeaaeio a?ae
iaeiai ia?aiao?a ioe?ieo /anoeiii? iio?aeii? ii ii/aoeiaiio cia/aiith;

ca aeiiiiiaith iaoiaeo ona?aaeiaiiy aeine?aeaeaii ?ica’yci?noue e?aeiaeo
caaea/ aeey aeayeeo eean?a nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ci?iiei
cai?ciaiiyi;

ca aeiiiiiaith iaoiaeo ona?aaeiaiiy aeine?aeaeaii ?ica’yci?noue e?aeiaeo
caaea/ aeey aeayeeo eean?a nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ci?iiei
iaiaaeaiei cai?ciaiiyi;

?icaeiooi /enaeueii-aiae?oe/iee iaoiae aeine?aeaeaiiy aeaioi/eiaeo
e?aeiaeo caaea/ aeey nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ia?aoai?aiei
a?aoiaioii;

aia?oa iaa?oioiaaii /enaeueii-aiae?oe/iee iaoiae aeine?aeaeaiiy e?aeiaeo
caaea/ aeey nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ia?aoai?aiei
a?aoiaioii o aeiaaeeo aaaaoioi/eiaeo ? ?ioaa?aeueieo e?aeiaeo oiia.

Aeinoia??i?noue io?eiaieo ?acoeueoao?a caaacia/o?oueny iayai?noth
no?iaeo iaoaiaoe/ieo aeiaaaeaiue.

?ic?iaeai? o aeena?oaoe?? iaoiaee aeine?aeaeaiiy iiaeooue aooe
ia?aianai? ia aiaeia?/i? eeane aeeoa?aioe?aeueieo ??aiyiue c a?aeoeeaiei
a?aoiaioii a?eueo caaaeueiiai aeaeyaeo, a io?eiai? ?acoeueoaoe –
aeei?enoai? i?e ?ica’ycoaaii? eiie?aoieo i?eeeaaeieo caaea/.

IA?AE?E IOAE?EAOe?E CA OAIITH AeENA?OAOe??

O?e?i/oe I.I., A?aoi ss.E. *enaeueii-aiae?oe/iee iaoiae aeine?aeaeaiiy
aaaaoioi/eiaeo e?aeiaeo caaea/ aeey nenoai aeeoa?aioe?aeueieo ??aiyiue
?c ia?aoai?aiei a?aoiaioii // Oe?. iao. aeo?i. – 1998. – O. 50, ? 11. –
N.1581-1585.

O?e?i/oe I.I. Ona?aaeiaiiy aeayeeo e?aeiaeo caaea/ aeey nenoai
aeeoa?aioe?aeueieo ??aiyiue ?c ci?iiei cai?ciaiiyi // Iae?i?ei?
eieeaaiiy. – 1998. – ? 2. – N.152-156.

A?aoi ss.E., O?e?i/oe I.I. Aneiioioe/ia ?ica’ycaiiy iaei??? e?aeiai?
caaea/? aeey nenoaie aeeoa?aioe?aeueieo ??aiyiue c cai?ciaiiyi //
Iae?i?ei? e?aeia? caaea/? iaoaiaoe/ii? o?ceee oa ?o canoinoaaiiy. –
*anoeia 2. – E.: ?i-o iaoaiaoeee IAI Oe?a?ie, 1996. – N.3-5.

O?e?i/oe I.I. *enaeueii-aiae?oe/iee iaoiae aeine?aeaeaiiy aeaioi/eiaeo
e?aeiaeo caaea/ aeey iae?i?eieo nenoai aeeoa?aioe?aeueieo ??aiyiue ?c
ci?iiei cai?ciaiiyi // ?ioaa?aeuei? ia?aoai?aiiy oa ?o canoinoaaiiy
aei e?aeiaeo caaea/. – E.: ?i-o iaoaiaoeee IAI Oe?a?ie, 1997. – Aei.
15. – N.238-251.

O?e?i/oe I.I. Iaa?oiooaaiiy iaoiaeo ona?aaeiaiiy aeey iaeiiai eeano
nenoai aeeoa?aioe?aeueieo ??aiyiue ?c ci?iiei cai?ciaiiyi // E?aeia?
caaea/? aeey aeeoa?aioe?aeueieo ??aiyiue. – E.: ?i-o iaoaiaoeee IAI
Oe?a?ie, 1998. – Aei.1(17). – N.254-259.

O?e?i/oe I.I. Ona?aaeiaiiy aaaaoioi/eiaeo e?aeiaeo caaea/ iaia??iaee/ieo
nenoai ?c ci?iiei cai?ciaiiyi // Iaoa??aee Nueiii? I?aei. iaoe. eiio.
?i. aeaaeai?ea I.E?aa/oea. – Ee?a, 1998. – N.500.

O?e?i/oe I.I. Canoinoaaiiy iaoiaeo ona?aaeiaiiy aei aeine?aeaeaiiy
aaaaoioi/eiaeo e?aeiaeo caaea/ aeey iaeiiai eeano nenoai
aeeoa?aioe?aeueieo ??aiyiue ?c ci?iiei iaiaaeaiei cai?ciaiiyi //
Iaoa??aee i?aei. iaoe. eiio. «No/ani? i?iaeaie iaoaiaoeee». – *anoeia 4.
– *a?i?aoe?: ?ooa, 1998. – N.108-111.

O?e?i/oe I.I. Aneiioioe/ia ?ica’ycaiiy iaei??? e?aeiai? caaea/? aeey
nenoaie aeeoa?aioe?aeueieo ??aiyiue c cai?ciaiiyi // Oace aeii. Anaoe?.
eiio. «Aeeoa?aioe?aeueii-ooieoe?iiaeuei? ??aiyiiy oa ?o canoinoaaiiy». –
Ee?a, 1996.– N. 189.

O?e?i/oe I.I. *enaeueii-aiae?oe/iee iaoiae aeine?aeaeaiiy e?aeiaeo
caaea/ aeey nenoai c cai?ciaiiyi // Intern. Conf. «Modelling and
investigation of systems stability». Thesis of conference reports. –
Kiev, 1997. – P. 120.

AIIOAOe??

O?e?i/oe I.I. Iaoiae ona?aaeiaiiy a e?aeiaeo caaea/ao aeey
aeeoa?aioe?aeueieo ??aiyiue c a?aeoeeaiei a?aoiaioii. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.01.02 –
aeeoa?aioe?aeuei? ??aiyiiy. – *a?i?aaoeueeee aea?aeaaiee oi?aa?neoao ?i.
TH.Oaaeueeiae/a, *a?i?aoe?, 1999.

Aeey aeeoa?aioe?aeueieo ??aiyiue c a?aeoeeaiei a?aoiaioii, ii/aoeiaa
iiiaeeia yeeo neeaaea?oueny ?c iaei??? oi/ee, o aeena?oaoe??
aeine?aeaeo?oueny ?ica’yci?noue e?aeiaeo caaea/.

-ieieao ?aeeieo ?ica’yce?a a?aeiia?aeieo ona?aaeiaieo e?aeiaeo caaea/.

Aeey iaia??iaee/ieo nenoai ?c ci?iiei cai?ciaiiyi a i?eiouaii? ?nioaaiiy
?aeeieo ?ica’yce?a aeo?aeieo oa ona?aaeiaieo aaaaoioi/eiaeo e?aeiaeo
caaea/ anoaiiaeaii oiiae, ye? aa?aioothoue ?o aeecuee?noue.

Aeey nenoai ?c ia?aoai?aiei a?aoiaioii iaa?oioiaaii
/enaeueii-aiae?oe/iee iaoiae aeine?aeaeaiiy e?aeiaeo caaea/ ?c
aeaioi/eiaeie, aaaaoioi/eiaeie oa ?ioaa?aeueieie e?aeiaeie oiiaaie.

Eeth/ia? neiaa: iaoiae ona?aaeiaiiy, e?aeiaa caaea/a, aeeoa?aioe?aeueia
??aiyiiy, a?aeoeeaiee a?aoiaio, ci?iia cai?ciaiiy, ia?aoai?aiee
a?aoiaio, /enaeueii-aiae?oe/iee iaoiae.

Oeeei/oe I.I. Iaoiae on?aaeiaiey a e?aaauo caaea/ao aeey
aeeooa?aioeeaeueiuo o?aaiaiee n ioeeiiythueiny a?aoiaioii. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.02 –
aeeooa?aioeeaeueiua o?aaiaiey. – *a?iiaeoeeee ainoaea?noaaiiue
oieaa?neoao ei. TH.Oaaeueeiae/a, *a?iiaoeu, 1999.

Aeey aeeooa?aioeeaeueiuo o?aaiaiee n ioeeiiythueiny a?aoiaioii,
ia/aeueiia iiiaeanoai eioi?uo ninoieo ec iaeiie oi/ee, a aeenna?oaoeee
enneaaeoaony ?ac?aoeiinoue e?aaauo caaea/.

-ie?anoiinoyo aaeeinoaaiiuo ?aoaiee niioaaonoaothueo on?aaeiaiiuo
e?aaauo caaea/. Enneaaeiaaiu oaeaea e?aaaua caaea/e n eeiaeiuie
aeaoooi/a/iuie e?aaauie oneiaeyie, niaea?aeaueie iaecaanoiue neaey?iue
ia?aiao?. Aeey iaia?eiaee/aneeo nenoai n ia?aiaiiui caiacaeuaaieai a
i?aaeiieiaeaiee nouanoaiaaiey aaeeinoaaiiuo ?aoaiee enoiaeiuo e
on?aaeiaiiuo iiiaioi/a/iuo e?aaauo caaea/ iieo/aiu oneiaey,
aa?aioe?othuea eo aeecinoue. Eae a ia?eiaee/aneii, oae e a
iaia?eiaee/aneii neo/ayo, caiacaeuaaiea a enoiaeiuo nenoaiao iiaeaoue
auoue iaia?aie/aiiui, iiyoiio iii nio?aiaii e a on?aaeiaiiie nenoaia.

-ie?anoiinoyo aaeeinoaaiiuo ?aoaiee niioaaonoaothueo on?aaeiaiiuo
e?aaauo caaea/. Enneaaeiaaiu oaeaea e?aaaua caaea/e n eeiaeiuie
aeaoooi/a/iuie e?aaauie oneiaeyie, niaea?aeaueie iaecaanoiue
neaey?iue ia?aiao?. Aeey iaia?eiaee/aneeo nenoai n ia?aiaiiui
ia?aie/aiiui caiacaeuaaieai a i?aaeiieiaeaiee nouanoaiaaiey
aaeeinoaaiiuo ?aoaiee enoiaeiuo e on?aaeiaiiuo iiiaioi/a/iuo e?aaauo
caaea/ iieo/aiu oneiaey, aa?aioe?othuea eo aeecinoue. Eae a
ia?eiaee/aneii, oae e a iaia?eiaee/aneii neo/ayo, on?aaeiaiiay nenoaia
ia niaea?aeeo caiacaeuaaiey.

Aeey nenoai n i?aia?aciaaiiui a?aoiaioii iainiiaai
/eneaiii-aiaeeoe/aneee iaoiae enneaaeiaaiey e?aaauo caaea/ a neo/aa
eeiaeiuo aeaoooi/a/iuo, iiiaioi/a/iuo, a oaeaea eioaa?aeueiuo e?aaauo
oneiaee. Aeey eaaeaeie ?anniao?eaaaiie caaea/e iino?iaia ?aaiiia?ii
noiaeyuayny iineaaeiaaoaeueiinoue ooieoeee, ii?aaeaeaia naycue
i?aaeaeueiie ooieoeee n oi/iui ?aoaieai, ia iniiaaiee naienoa
i?eaeeaeaiiuo ii?aaeaeythueo o?aaiaiee iieo/aiu aeinoaoi/iua e
iaiaoiaeeiua oneiaey ?ac?aoeiinoe e?aaaie caaea/e. Aeey eaaeaeie e?aaaie
caaea/e aeiiieieoaeueii i?aaeeiaeaia noaia /eneaiii-aiaeeoe/aneiai
iaoiaea aac ii?aaeaeythuaai o?aaiaiey.

Eeth/aaua neiaa: iaoiae on?aaeiaiey, e?aaaay caaea/a,
aeeooa?aioeeaeueiia o?aaiaiea, ioeeiiythueeny a?aoiaio, ia?aiaiiia
caiacaeuaaiea, i?aia?aciaaiiue a?aoiaio, /eneaiii-aiaeeoe/aneee iaoiae.

Filipchuk M.P. Averaging method in the boundary value problems for
differential equations with deviated argument. – Manuscript.

Dissertation for candidate’s degree by speciality 01.01.02 –
differential equations. – Chernivtsi State University named by Yu.
Fedkovych, Chernivtsi, 1999.

The solvability of boundary value problems in dissertation is
investigated for differential equations with deviated argument initial
set of which contains one point.

-vicinities of unique solutions of respective averaging boundary value
problems were obtained for periodic systems with variable delay.

Assuming existence and uniqueness of solutions of original and averaging
multipoint boundary value problems, the conditions which assure their
closeness were obtained for nonperiodic systems with variable delay.

The numerical-analytic method of investigation of boundary value
problems with twopoint, multipoint and integral boundary conditions was
substantiated for systems with transformed argument.

Key words: averaging method, boundary value problem, differential
equation, deviated argument, variable delay, transformed argument,
numerical-analytic method.

Нашли опечатку? Выделите и нажмите CTRL+Enter

Похожие документы
Обсуждение

Ответить

Курсовые, Дипломы, Рефераты на заказ в кратчайшие сроки
Заказать реферат!
UkrReferat.com. Всі права захищені. 2000-2020