An hp-version Spectral Collocation Method for Nonlinear Volterra Integro-differential Equation with Weakly Singular Kernels

被引：26

作者：

Wang, Chuan-Li ^{[1
,4
]}

Wang, Zhong-Qing ^{[2
]}

Jia, Hong-Li ^{[3
]}

机构：

[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China

[2] Univ Shanghai Sci & Technol, Coll Sci, Shanghai 200093, Peoples R China

[3] Donghua Univ, Dept Math, Shanghai 200063, Peoples R China

[4] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China

来源：

JOURNAL OF SCIENTIFIC COMPUTING | 2017年 / 72卷 / 02期

基金：

中国国家自然科学基金;

关键词：

hp-version spectral collocation method; Nonlinear Volterra integro-differential equations; Weakly singular kernels; Convergence analysis; INTEGRO-DIFFERENTIAL-EQUATIONS; POLYNOMIAL SPLINE COLLOCATION; DISCONTINUOUS GALERKIN METHOD; RUNGE-KUTTA METHODS; CONVERGENCE ANALYSIS;

D O I：

10.1007/s10915-017-0373-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present an hp-version Legendre-Jacobi spectral collocation method for the nonlinear Volterra integro-differential equations with weakly singular kernels. We derive hp-version error bounds of the collocation method under the -norm for the Volterra integro-differential equations with smooth solutions on arbitrary meshes and singular solutions on quasi-uniform meshes. Numerical experiments demonstrate the effectiveness of the proposed method.

引用

页码：647 / 678

页数：32

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