Asymptotics of integrodifferential models with integrable kernels

Bijura, Angelina M.

doi:10.1155/s0161171203209091

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2023

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Cited by 4 publications

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“…which is a Volterra integral equation of the second kind. Singularly perturbed Volterra integro-differential equations arise in many physical and biological problems (see, e.g., [1][2][3][4][5][6][7]). A survey of singularly perturbed Volterra integral and integro-differential equations is provided in [8].…”

Section: Introductionmentioning

confidence: 99%

The coupled method for singularly perturbed Volterra integro-differential equations

Tao

Zhang

2019

Adv Differ Equ

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In this work a coupled (LDG-CFEM) method for singularly perturbed Volterra integro-differential equations with a smooth kernel is implemented. The existence and uniqueness of the coupled solution is given, provided that the source function and the kernel function are sufficiently smooth. Furthermore, the coupled solution achieves the optimal convergence rate p + 1 in the L 2 norm and a superconvergence rate 2p at nodes for the numerical solutionÛ N with the one-sided flux inside the boundary layer region under layer-adapted meshes uniformly with respect to the singular perturbation parameter .

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