Numerical implementation of solving a boundary value problem with parameter for Fredholm integro-differential equation

Elmira Bakirova; Narkesh Iskakova; Zhazira Kadirbayeva

doi:10.70474/rxzvna18

Авторлар

Эльмира Айнабековна Бакирова Математика және математикалық модельдеу институты Author https://orcid.org/0000-0002-3820-5373
Наркеш Билаловна Искакова Математика және математикалық модельдеу институты Author https://orcid.org/0000-0002-0680-4099
Жазира Муратбековна Кадирбаева Математика және математикалық модельдеу институты Author https://orcid.org/0000-0001-8861-4100

DOI:

https://doi.org/10.70474/rxzvna18

Кілт сөздер:

интегралдық-дифференциалдық теңдеу, шеттiк есеп, параметрлеу әдiсi, параметр, шешiлiмдiлiк

Аңдатпа

Жұмыста өзегi айныған Фредгольм интегралдық-дифференциалдық теңдеуi үшiн параметрi бар шеттiк есеп зерттелiнедi. Жұмыстың мақсаты зерттелiнетiн есептiң бiрмәндi шешiлiмдiлiгiн, аналитикалық және сандық шешiмдерiн құру болып табылады. Мақсатқа жету негiзi болып Джумабаевтың параметрлеу әдiсi, Коши есептерiн шешудiң классикалық сандық әдiстерi және сандық интегралдаудың тәсiлдерi жатады. Қосымша параметрдi және жаңа белгiсiз функцияны енгiзу арқылы параметрлерi бар есеп алынады. Қарастырылып отырған теңдеудiң, шеттiк шарттардың бастапқы берiлiмдерi бойынша параметрлерге қатысты теңдеулер жүйесi құрылады. Белгiсiз функция жәй дифференциалдық теңдеу үшiн Коши есебiнiң шешiмi ретiнде табылады. Бастапқы есеп пен параметрлерi бар есептiң эквиваленттiлiгi, бiрмәндi шешiлiмдiлiгiнiң шарттары тағайындалады және аналитикалық шешiмдi табудың формуласы алынады. Берiлген есептiң аналитикалық және жуық шешiмдерiн табудың тесттiк мысалдары келтiрiледi.

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