A multi-domain spectral collocation method for Volterra integral equations with a weakly singular kernel

被引：14

作者：

Ma, Zheng ^{[1
]}

Alikhanov, Anatoly A. ^{[2
]}

Huang, Chengming ^{[1
,3
]}

Zhang, Guoyu ^{[4
]}

机构：

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] North Caucasus Fed Univ, Pushkin Str 1, Stavropol 355017, Russia

[3] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Peoples R China

[4] Inner Mongolia Univ, Sch Math Sci, Hohhot 010021, Peoples R China

来源：

APPLIED NUMERICAL MATHEMATICS | 2021年 / 167卷

基金：

中国国家自然科学基金;

关键词：

Volterra integral equation; Weakly singular kernel; Multi-domain spectral collocation; Nonpolynomial collocation; Graded mesh; Error analysis; NUMERICAL-SOLUTIONS; HP-VERSION; INTEGRODIFFERENTIAL EQUATIONS; SPLINE COLLOCATION; SUPERCONVERGENCE; APPROXIMATION; SMOOTH;

D O I：

10.1016/j.apnum.2021.05.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a multi-domain Muntz-polynomial spectral collocation method with graded meshes for solving second kind Volterra integral equations with a weakly singular kernel. This method is particularly suitable for problems whose solutions contain non-integer exponent factors. We carry out a rigorous error analysis of hp-version in the L-infinity- and weighted L-2-norms. Several numerical examples are presented to demonstrate the efficiency and accuracy of the method. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：218 / 236

页数：19

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