Numerical Solutions for Weakly Singular Volterra Integral Equations Using Chebyshev and Legendre Pseudo-Spectral Galerkin Methods

Li, Xianjuan1; Tang, Tao2,3,4; Xu, Chuanju5,6

2016-04

10.1007/s10915-015-0069-5

JOURNAL OF SCIENTIFIC COMPUTING   影响因子和分区

0885-7474

1573-7691

In this paper we present and analyze Chebyshev and Legendre pseudo-spectral methods for the second kind Volterra integral equations with weakly singular kernel (x - s)(-mu), 0 < mu < 1. The proposed methods are based on the Gauss-type quadrature formula for approximating the integral operators involved in the equations. The present work is an extension of the earlier proposed spectral Jacobi-Galerkin method for the second kind Volterra integral equations with regular kernels (Xie et al. in J Sci Comput 53(2):414-434, [21]). Adetailed convergence analysis is carried out, and several error estimates in L-infinity and L-omega(2) norms are obtained. Numerical examples are considered to verify the theoretical predictions.

SCI ; EI

英语

其他

Fuzhou University[0460022456]

Mathematics

Mathematics, Applied

WOS:000374416400003

SPRINGER/PLENUM PUBLISHERS

20161202133414

Galerkin methods ; Numerical methods

Calculus:921.2 ; Numerical Methods:921.6

MATHEMATICS

Web of Science

1.Fuzhou Univ, Coll Math & Comp Sci, Fuzhou 350108, Peoples R China
2.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China
3.Hong Kong Baptist Univ, Inst Computat & Theoret Studies, Kowloon Tong, Hong Kong, Peoples R China
4.South Univ Sci & Technol, Dept Math, Shenzhen 518055, Guangdong, Peoples R China
5.Xiamen Univ, Sch Math Sci, Xiamen 361005, Peoples R China
6.Xiamen Univ, Fujian Prov Key Lab Math Modeling & High Performa, Xiamen 361005, Peoples R China

Li, Xianjuan,Tang, Tao,Xu, Chuanju. Numerical Solutions for Weakly Singular Volterra Integral Equations Using Chebyshev and Legendre Pseudo-Spectral Galerkin Methods[J]. JOURNAL OF SCIENTIFIC COMPUTING,2016,67(1):43-64.

Li, Xianjuan,Tang, Tao,&Xu, Chuanju.(2016).Numerical Solutions for Weakly Singular Volterra Integral Equations Using Chebyshev and Legendre Pseudo-Spectral Galerkin Methods.JOURNAL OF SCIENTIFIC COMPUTING,67(1),43-64.

Li, Xianjuan,et al."Numerical Solutions for Weakly Singular Volterra Integral Equations Using Chebyshev and Legendre Pseudo-Spectral Galerkin Methods".JOURNAL OF SCIENTIFIC COMPUTING 67.1(2016):43-64.