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Article · International Journal of Mathematics and Physics · June 25, 2018

Asymptotic convergence of the solution of the initial value problem for singularly perturbed higher-order integro-differential equation

M. K. Dauylbayev, Marat U. Akhmet, A. E. Mirzakulova, A. B. Uaissov

Aziza Mirzakulova
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Abstract

Abstract. The article is devoted to research the Cauchy problem for singularly perturbed higher-order linear integro-differential equation with a small parameters at the highest derivatives, provided that the roots of additional characteristic equation have negative signs. An explicit analytical formula of the solution of singularly perturbed Cauchy problem is obtained. The theorem about asymptotic estimate of a solution of the initial value problem is proved. The nonstandard degenerate initial value problem is constructed. We find the solution of the nonstandard degenerate initial value problem. An estimate difference of the solution of a singularly perturbed and nonstandard degenerate initial value problems is obtained. The asymptotic convergence of solution of a singularly perturbed initial value problem to the solution of the nonstandard degenerate initial value problem is established. G M T Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский Английский Испанский Итальянский Казахский Китайский Трад Китайский Упр Корейский Русский Турецкий Французский Звуковая функция ограничена 200 символами Настройки : История : Обратная связь : Donate Закрыть

Differential Equations and Numerical MethodsDifferential Equations and Boundary ProblemsNonlinear Differential Equations Analysissingularly perturbed integro-differential equationsinitial value problemsasymptotic convergence

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