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Чисельні методи оптимізації та моделювання в псевдогіперболічних системах: Автореф. дис… канд. фіз.-мат. наук / Д.А. Номіровський, НАН України. Ін-т

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Iaoe?iiaeueia aeaaeai?y iaoe Oe?a?ie

?inoeooo e?aa?iaoeee ?iai? A.I. Aeooeiaa

III??IANUeEEE Aeieo?i Aiaoie?eiae/

OAeE 517.977.58

*enaeuei? iaoiaee iioei?caoe?? oa iiaeaethaaiiy

a inaaaeia?ia?aie?/ieo nenoaiao

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

Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a 1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia ia eaoaae?? ia/enethaaeueii? iaoaiaoeee oaeoeueoaoo
e?aa?iaoeee Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana Oaa/aiea

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Eyoei Na?a?e ?aaiiae/,

Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea,

oaeoeueoao e?aa?iaoeee, caa?aeoaa/ eaoaae?e

ia/enethaaeueii? iaoaiaoeee

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe, i?ioani?

Ee?e/aiei Ieeiea Oaaei?iae/,

?inoeooo e?aa?iaoeee ?i. A.I. Aeooeiaa

IAI Oe?a?ie, i?ia?aeiee iaoeiaee ni?a?ia?oiee

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

C?iueei Iao?i Ieeieaeiae/,

Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea,

canooiiee aeaeaia c o/aiai? ?iaioe oaeoeueoaoo

e?aa?iaoeee EO, eaoaae?a NAOI?

I?ia?aeia onoaiiaa: ?inoeooo eini?/ieo aeine?aeaeaiue IAI oa IEA

Oe?a?ie, a?aeae?e iiaeaethaaiiy aeeiai?/ieo

i?ioean?a Caie? oa ieaiao, i. Ee?a

Caoeno a?aeaoaeaoueny ” 28 ” o?aaiy 1999 ?. i 11-00 aiae. ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.194.02 i?e ?inoeooo? e?aa?iaoeee
?iai? A.I.Aeooeiaa IAI Oe?a?ie ca aae?anith: 252022, Ee?a 22, i?iniaeo
Aeaaeai?ea Aeooeiaa, 40.

C aeena?oaoe??th iiaeia iciaeiieoeny a iaoeiai-oaoi?/iiio a?o?a?
?inoeoooo.

Aaoi?aoa?ao ?ic?neaiee ” 9 ” ea?oiy 1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee Neiyanueeee A.O.

Aeooaeuei?noue oaie. Caaea/? iioei?caoe?? oa iiaeaethaaiiy a e?i?eieo
nenoaiao neeaaeathoue iaeei c iaea?eueo aeooaeueieo iai?yie?a ?icaeoeo
i?eeeaaeii? iaoaiaoeee oa e?aa?iaoeee, na?aae yeeo cia/ia i?noea caeia?
oai??y iioeiaeueiiai ea?oaaiiy ?iciiae?eaieie nenoaiaie oa ?ic?iaea
/enaeueieo iaoiae?a iaaeeaeaiiai ?ica’ycaiiy oeeo caaea/. O aaaaoueio
i?eeeaaeieo aeiaaeeao (canoinoaaiiy eaca?ii?, ?iioeuenii? oaoi?ee a
iaaeeoeei? oa ia?iaeiiio ainiiaea?noa?, ea?oaaiiy eini?/ieie aia?aoaie,
i?iaeooaaiiy nenoai i?e?ic?ioaiiy a?oioo, iiaa?oiaaiai caaa?oiaoaaiiy
iaoaeo, ?iciianthaeaeaiiy caa?oaeiaiue c i?noey aeieia?/ii? eaoano?ioe
oa ?i.) aieea ia nenoaio iineoue cina?aaeaeaiee oa?aeoa?, ui
i?ecaiaeeoue aei iiyae o i?aa?e /anoei? ??aiyiiy nenoaie ocaaaeueiaii?
ooieoe?? ? aeiaaa? ?ic?iaee niaoe?aeueieo i?aeoiae?a aei iioei?caoe?? oa
iiaeaethaaiiy oaeeie nenoaiaie.

C ?ioiai aieo, aeaye? o?ce/i? i?ioeane (?iciianthaeaeaiiy cao?aiue o
a’yceiio aac?, e?ooeeuei? eieeaaiiy a noa?aei? c aioo??oi?i oa?oyi,
i?a?aoe?y o?i?/ieo ?a/iaei c o?aooaaiiyi no?oeoo?e na?aaeiaeua oa ?i.)
ia aaeaeaaoii iiaeaeththoueny ca aeiiiiiaith a?aeiieo ??aiyiue
iaoaiaoe/ii? o?ceee ae?oaiai ii?yaeeo, ui aeiaaa? caeo/aoe aei ?icaeyaeo
iaeeane/i? inaaaeia?ia?aie?/i? iiaeae?. Oae, aeey nenoaie,
ooieoe?iioaaiiy yei? iieno?oueny aeeoa?aioe?aeueieie ??aiyiiyie c
/anoeiieie iio?aeieie inaaaeia?ia?aie?/iiai oeio, ?ai?oa ia
aeine?aeaeoaaany aaaeeeaee aeey i?aeoe/ieo canoinoaaiue aeiaaeie ae?oai?
i?oaii? caaea/?.

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith aeena?oaoe?eii? ?iaioe ?
aeine?aeaeaiiy iiaeaeae oa ?ic?iaea /enaeueieo iaoiae?a ocaaaeueiaii?
iioei?caoe?? nenoaie, ooieoe?iioaaiiy yei? iieno?oueny ae?oaith i?oaiith
caaea/ath aeey inaaaeia?ia?aie?/iiai aeeoa?aioe?aeueiiai iia?aoi?a. Aeey
oeueiai iio??aii iiaoaeoaaoe oai??th ocaaaeueiaii? ?ica’yciino? oeacaii?
e?aeiai? caaea/?, ciaeoe oiiae ea?iaaiino? oa ?nioaaiiy iioeiaeueiiai
ea?oaaiiy aeey eiie?aoieo caaea/ ocaaaeueiaiiai ea?oaaiiy (?iioeueniiai,
oi/eiaiai, ?ooiiiai oa ?i.), a?aeooeaoe a?aae??io ooieoe?iiaeo yeino?,
aeine?aeeoe eiai aeaaee?noue oa ?iciianthaeeoe io?eiai? ?acoeueoaoe ia
yeiiiaa oe?oee eean caaea/ ocaaaeueiaiiai ea?oaaiiy.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a. Aeey iiaeaeae, ui iienothoueny
ae?oaith i?oaiith caaea/ath aeey inaaaeia?ia?aie?/iiai iia?aoi?a,
io?eiaii aeae?eueea oei?a ai??i?ieo ia??aiinoae a iaaaoeaieo ii?iao oa
iiaoaeiaaii oai??th ocaaaeueiaii? ?ica’yciino?. Ciaeaeaii oiiae
ea?iaaiino? oa ?nioaaiiy iioeiaeueiiai ea?oaaiiy nenoaiith /a?ac i?aao
/anoeio ??aiyiiy oa eiao?oe??ioe. Aeine?aeaeaii ieoaiiy aeaaeeino?
aeayeeo e?eoa???a yeino? aeey oe?ieiai eeano ea?oth/eo ooieoe?e, ui aea?
iiaeeea?noue canoiniaoaaoe /enaeuei? iaoiaee a?aae??ioiiai oeio.
Cai?iiiiiaaii i?ioeaaeo?o ?aaoey?ecaoe?? ea?oth/i? ooieoe??.
Aeine?aeaeaii ieoaiiy ia/enethaaeueii? no?eeino? iaoiae?a a?aae??ioiiai
oeio.

I?aeoe/ia cia/aiiy ?acoeueoao?a. Iaa?oioiaaii iiaeeea?noue canoinoaaiiy
/enaeueieo iaoiae?a aeey ?ica’ycaiiy caaea/ iiaeaethaaiiy oa
ocaaaeueiaiiai ea?oaaiiy inaaaeia?ia?aie?/ieie nenoaiaie (ae?oaa i?oaia
caaea/a). Aeey ?ica’ycaiiy e?aeiai? caaea/? cai?iiiiiaaii aiaeia iaoiaeo
Aaeuei?e?ia, aeiaaaeaii eiai neeueio ca?aei?noue.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iaoa??aee aeena?oaoe??
aeiiia?aeaeeny ia i?aeia?iaei?e eiioa?aioe?? “No/ani? i?iaeaie oai???
o?eueo?aoe??” iai’yo? I.O. O?eue/aeiaa (??aia, 1998); 3-e Oe?a?inuee?e
eiioa?aioe?? c aaoiiaoe/iiai ea?oaaiiy “Aaoiiaoeea-96” (Naaanoiiieue,
1996); Oe?a?inuee?e eiioa?aioe?? “Iiaeaee?iaaiea e enneaaeiaaiea
onoie/eainoe nenoai” (Ee?a, 1996); iaoeiaeo eiioa?aioe?yo ani??aio?a oa
i?ioani?nueei-aeeeaaeaoeueeiai neeaaeo Ee?anueeiai oi?aa?neoaoo ?iai?
Oa?ana Oaa/aiea, oaeoeueoao e?aa?iaoeee (i. Ee?a, 1997, 1998); iaoeiaeo
nai?ia?ao c iiceoeaieie a?aeaoeaie “Iiaeaethaaiiy i?iaeai aeieiai? oa
aia?aaoeee” ?inoeoooo e?aa?iaoeee ?i. A.I. Aeooeiaa IAI Oe?a?ie (ea?.
A.A. Neiiaoeueeee); “*enaeuei? iaoiaee iioei?caoe??” ?inoeoooo
i?eeeaaeiiai ? nenoaiiiai aiae?co (ea?. A.I. Ioaie/iee);
“Ia/enethaaeueia iaoaiaoeea” eaoaae?e II (ea?. N.?. Eyoei) oa “Nenoaiiee
aiae?c oa oai??y i?eeiyooy iioeiaeueieo ??oaiue” eaoaae?e NAOI?
oaeoeueoaoo e?aa?iaoeee Ee?anueeiai oi?aa?neoaoo (ea?. I.A. Iaeiia/iee).

Ioae?eaoe??. Iniiai? iieiaeaiiy aeena?oaoe?? aena?oeaii o ainueie
iaoeiaeo ?iaioao, c yeeo i’youe noaoae iaae?oeiaaii a iaoeiaeo aeo?iaeao
Oe?a?ie, iaeio aeaiiiiaaii a AeIOA Oe?a?ie oa aea? iaoeia? ?iaioe — a
ca??ieeao oac aeiiia?aeae eiioa?aioe?e.

Iniaenoee aianie aeena?oaioa a ?iaioao, aeeiiaieo o ni?aaaoi?noa?
iieyaa? a ciaoiaeaeaii? oiia oai?aie, ui a?aeiinyoueny aei ioieoo
“Aeeooa?aioeeaeueiua naienoaa e?eoa?ey ea/anoaa” noaoo? [3], a
noaoo? [4] ciaeaeaii oiiae oa aeiaaaeaii oai?aio ?nioaaiiy iioeiaeueiiai
?ooiiiai ea?oaaiiy, a noaoo? [5] aaoi?o iaeaaeaoue ?aea? aeiaaaeaiiy
oai?ai i?i iioeiaeueia ?ooiia ea?oaaiiy ? aeiaaaeaiiy oe??? oai?aie a
a?eueo i?inoiio aeiaaeeo, a noaoo? [6] ciaeaeaii aeiaaaeaiiy ai??i?ii?
ia??aiino? a iaaaoeaieo ii?iao.

No?oeoo?a oa ianya aeena?oaoe??. Aeena?oaoe?eia ?iaioa neeaaea?oueny ?c
anooio, o?ueio ?icae?e?a, aeniiae?a, nieneo e?oa?aoo?e oa aeiaeaoeo.
Caaaeueiee ianya ?iaioe neeaaea? 157 noi??iie. A?ae?ia?ao?y i?noeoue 78
iaeiaioaaiue.

Ci?no aeena?oaoe?eii? ?iaioe

O anooi? iaa?oioiao?oueny aeooaeuei?noue oaie, oi?ioeth?oueny iaoa,
aeaco?oueny iaoeiaa iiaecia aeine?aeaeaiiy.

O ia?oiio ?icae?e? “Iiaeae? inaaaeia?ia?aie?/iiai oeio. Ae?oaa i?oaia
caaea/a” aeine?aeaeo?oueny ieoaiiy ocaaaeueiaii? ?ica’yciino? oeacaii?
caaea/?.

O aaaaoueio no/anieo iaoeiaeo aeine?aeaeaiiyo ?icaeyaeathoue nenoaie,
ooieoe?iioaaiiy yeeo iieno?oueny ??aiyiiyie

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???u?th??????Ii?yae c caaaeueiei ??aiyiiyi (1) aeine?aeaeothoueny
eiai aeaui ni?iuai? aa??aioe, aeey yeeo aaea?oueny io?eiaoe a?eueo
ci?noiai? ?acoeueoaoe

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?MathType??P????u?th??????Aiaeia?/i? ia??aiino? iathoue i?noea aeey
ni?yaeaiiai iia?aoi?a.

Ca eiaeiith ia??ai?noth eaie aeiaiaeyoueny oai?aie ?nioaaiiy oa
?aeeiino? ocaaaeueiaiiai ?ica’yceo. ?icaeyiaii, iai?eeeaae, aeiaaeie
ia?oi? ia??aiino?.

Icia/aiiy 3. Ocaaaeueiaiei ?ica’yceii (1) iaceaa?oueny oaea ooieoe?y
wmetafile8? ??O???????????
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ia??aiinoyo eaie 1 aea? iiaeeea?noue ?icaeyaeaoe ?icoe?aiiy iia?aoi??a
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?ica’yciino? ca ?ioeie ia??aiinoyie eaie 1.

Ae?oaee ?icae?e ?iaioe — “Iioeiaeueia ea?oaaiiy a inaaaeia?ia?aie?/ieo
iiaeaeyo” — i?enay/aiee aeine?aeaeaiith ieoaiiy ea?iaaiino? oa ?nioaaiiy
iioeiaeueiiai ea?oaaiiy nenoaiith /a?ac i?aao /anoeio oa eiao?oe??ioe
??aiyiiy.

Iaoae noai nenoaie caaeiaieueiy? ??aiyiiy wmetafile8?
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Caoaaaeaiiy. Caaaeath/e ia oa, ui a caaaeueiiio aeiaaeeo a?aeia?aaeaiiy
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aeey aeia?eueii? nenoaie, ui caaeiaieueiy? ia??aiinoyi a iaaaoeaieo
ii?iao.

O ?iaio? ?icaeyaea?oueny na??y aiaeia?a oai?aie 4 aeey ?ioeo
ooieoe?iiae?a yeino? oa aeey aeiaaeeo caaea/? ea?oaaiiy eiao?oe??ioaie
??aiyiiy.

?icaeyiooi canoinoaaiiy oai?aie 4 oa ?? aiaeia?a aeey aeine?aeaeaiiy
caaea/ c ?iioeueniei, oi/eiaei, ?iioeuenii-oi/eiaei, ?ooiiei oa aeayeeie
?ioeie oeiaie ea?oth/i? ooieoe??.

?icaeyiaii ieoaiiy ea?iaaiino?

Icia/aiiy 5. Aoaeaii iaceaaoe nenoaio ea?iaaiith (aneiioioe/ii
ea?iaaiith) a

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