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

Date

2018-01-01

Author

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

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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.

Subject Keywords

singular perturbation, small parameter, the initial functions, asymptotics, passage to the limit

URI

https://hdl.handle.net/11511/99138

Journal

INTERNATIONAL JOURNAL OF MATHEMATICS AND PHYSICS

Collections

Department of Mathematics, Article

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Citation Formats

M. K. Dauylbayev, M. Akhmet, A. E. Mirzakulova, and A. B. Uaissov, “Asymptotic convergence of the solution of the initial value problem for singularly perturbed higher-order integro-differential equation,” INTERNATIONAL JOURNAL OF MATHEMATICS AND PHYSICS, vol. 9, no. 1, pp. 50–59, 2018, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/99138.