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Numerical Algorithms
Published in: Numerical Algorithms 2/2020

15-11-2019 | Original Paper

The asymptotic approximations to linear weakly singular Volterra integral equations via Laplace transform

Authors: Tongke Wang, Meng Qin, Huan Lian

Published in: Numerical Algorithms | Issue 2/2020

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Abstract

In this paper, the asymptotic expansions for the solution about zero and infinity are formulated via Laplace transform for linear Volterra integral equation with weakly singular convolution kernel. The expansions about zero and infinity, as well as their Padé approximations, are used to approximate the solution when the argument is small and large, respectively, and the Padé approximations are more accurate. The methods are also valid to solve some other Volterra type integral equations including linear Volterra integro-differential equations, fractional integro-differential equations, and system of singular Volterra integral equations of the second kind with convolution kernels. Some examples confirm the correctness of the methods and the effectiveness of the asymptotic expansions. They show that numerical methods are only necessary in a small interval in practical computation when uniform high precision evaluations are needed for solving these kinds of Volterra integral equations.
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Metadata
Title
The asymptotic approximations to linear weakly singular Volterra integral equations via Laplace transform
Authors
Tongke Wang
Meng Qin
Huan Lian
Publication date
15-11-2019
Publisher
Springer US
Published in
Numerical Algorithms / Issue 2/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-019-00832-5

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