Spectral methods for weakly singular Volterra integral equations with pantograph delays

被引：31

作者：

Zhang, Ran ^{[1
]}

Zhu, Benxi ^{[1
]}

Xie, Hehu ^{[2
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

[2] Chinese Acad Sci, LSEC, NCMIS, Inst Computat Math,Acad Math & Syst Sci, Beijing 100190, Peoples R China

来源：

FRONTIERS OF MATHEMATICS IN CHINA | 2013年 / 8卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Volterra integral equation; vanishing delay; weakly singular kernel; Jacobi-spectral collocation method; error analysis; POLYNOMIAL-APPROXIMATION; DIFFERENTIAL-EQUATIONS; COLLOCATION METHODS; CONVERGENCE; INTERPOLATION; SYSTEMS;

D O I：

10.1007/s11464-013-0282-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the convergence analysis of the Volterra integral equation of second kind with weakly singular kernel and pantograph delays is provided. We use some function transformations and variable transformations to change the equation into a new Volterra integral equation with pantograph delays defined on the interval [-1, 1], so that the Jacobi orthogonal polynomial theory can be applied conveniently. We provide a rigorous error analysis for the proposed method in the L (a)-norm and the weighted L (2)-norm. Numerical examples are presented to complement the theoretical convergence results.

引用

页码：281 / 299

页数：19

共 50 条

[1] Spectral methods for weakly singular Volterra integral equations with pantograph delays
Ran Zhang
Benxi Zhu
Hehu Xie
[J]. Frontiers of Mathematics in China, 2013, 8 : 281 - 299
[2] Spectral methods for weakly singular Volterra integral equations with smooth solutions
Chen, Yanping
Tang, Tao
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 233 (04) : 938 - 950
[3] JACOBI SPECTRAL GALERKIN METHODS FOR VOLTERRA INTEGRAL EQUATIONS WITH WEAKLY SINGULAR KERNEL
Yang, Yin
[J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2016, 53 (01) : 247 - 262
[4] A hybrid spectral method for the nonlinear Volterra integral equations with weakly singular kernel and vanishing delays
Yao, Guoqing
Tao, DongYa
Zhang, Chao
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2022, 417
[5] Jacobi Spectral Galerkin Methods for a Class of Nonlinear Weakly Singular Volterra Integral Equations
Kant, Kapil
Mandal, Moumita
Nelakanti, Gnaneshwar
[J]. ADVANCES IN APPLIED MATHEMATICS AND MECHANICS, 2021, 13 (05) : 0163 - 1260
[6] Convergence analysis of spectral collocation methods for a class of weakly singular Volterra integral equations
Ma, Xiaohua
Huang, Chengming
Niu, Xin
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2015, 250 : 131 - 144
[7] Parallel methods for weakly singular Volterra integral equations on GPUs
Conte, Dajana
Paternoster, Beatrice
[J]. APPLIED NUMERICAL MATHEMATICS, 2017, 114 : 30 - 37
[8] Spectral collocation method for system of weakly singular Volterra integral equations
Zhendong Gu
[J]. Advances in Computational Mathematics, 2019, 45 : 2677 - 2699
[9] Spectral collocation method for system of weakly singular Volterra integral equations
Gu, Zhendong
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2019, 45 (5-6) : 2677 - 2699
[10] On systems of volterra difference equations associated with collocation methods for weakly singular Volterra integral equations
Brunner, H
[J]. NEW DEVELOPMENTS IN DIFFERENCE EQUATIONS AND APPLICATIONS, 1999, : 75 - 92

← 1 2 3 4 5 →