Spectral Collocation Methods for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels

被引：20

作者：

Yang, Yin ^{[1
]}

Chen, Yanping ^{[2
]}

机构：

[1] Xiangtan Univ, Sch Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

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

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2019年 / 42卷 / 01期

关键词：

Spectral collocation method; Nonlinear; Volterra integro-differential equations; CONVERGENCE ANALYSIS; INTEGRAL-EQUATIONS; POLYNOMIAL-APPROXIMATION; INTERPOLATION;

D O I：

10.1007/s40840-017-0487-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A spectral Jacobi-collocation approximation is proposed and analyzed for nonlinear integro-differential equations of Volterra type with weakly singular kernel, and a rigorous error analysis is provided for the spectral methods to show both the errors of approximate solutions and the errors of approximate derivatives of the solutions decaying exponentially in infinity-norm and weighted L2-norm. Numerical results are presented to confirm the theoretical prediction of the exponential rate of convergence.

引用

页码：297 / 314

页数：18

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