A Legendre spectral method for multidimensional partial Volterra integro-differential equations

被引：9

作者：

Zheng, Weishan ^{[1
]}

Chen, Yanping ^{[2
]}

Zhou, Jianwei ^{[3
]}

机构：

[1] Hanshan Normal Univ, Coll Math & Stat, Chaozhou 521041, Guangdong, Peoples R China

[2] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

[3] Linyi Univ, Sch Math & Stat, Linyi 276005, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2024年 / 436卷

基金：

中国国家自然科学基金;

关键词：

Volterra integro-differential equations; Legendre spectral method; Exponential convergence; Reliability; Gauss-Legendre quadrature rule; POLYNOMIAL-APPROXIMATION; COLLOCATION METHODS; 4TH-ORDER EQUATION; INTEGRAL-EQUATIONS; CONVERGENCE;

D O I：

10.1016/j.cam.2023.115302

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a Legendre spectral method for solving multidimensional partial Volterra integro-differential equations. The main idea of our approach is first to employ some function transformations and variable transformations to transform the equations into new partial Volterra integro-differential equations, and then the Legendre spectral method is used to solve the equivalent equations. We derive error bounds in L-infinity- and L-2-norms, which indicate that the errors of solution and the first order partial derivative decay exponentially. Three numerical examples are displayed to confirm the reliability of the Legendre spectral analysis. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：17

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