An $ hp $-version spectral collocation method for fractional Volterra integro-differential equations with weakly singular kernels-Reference-Cited by-同舟云学术

An $ hp $-version spectral collocation method for fractional Volterra integro-differential equations with weakly singular kernels

Published:2023 Issue:8 Volume:8 Page:19816-19841
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Wang Chuanli¹,Chen Biyun²

Affiliation:

1. School of Mathematics and Statistics, Yancheng Teachers University, Yancheng 224007, China

2. School of Information Engineering, Yancheng Teachers University, Yancheng 224007, China

Abstract

<abstract><p>We present a multi-step spectral collocation method to solve Caputo-type fractional integro-differential equations (FIDEs) involving weakly singular kernels. We reformulate the problem as the second type Volterra integral equation (VIE) with two different weakly singular kernels. Based on these integral equations, we construct a multi-step Legendre-Gauss spectral collocation scheme for the problem. The $ hp $-version convergence is established rigorously. To demonstrate the effectiveness of the suggested method and the validity of the theoretical results, the results of some numerical experiments are presented.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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