Collocation and iterated collocation methods for a class of weakly singular Volterra integral equations

被引：41

作者：

Diogo, Teresa ^{[1
]}

机构：

[1] Univ Tecn Lisboa, Inst Super Tecn, Ctr Matemat & Aplicacoes, P-1049001 Lisbon, Portugal

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 229卷 / 02期

关键词：

Volterra integral equation; Singular kernel; Collocation methods; Iterated collocation; PIECEWISE POLYNOMIAL COLLOCATION; NUMERICAL-SOLUTION; 2ND KIND; KERNELS;

D O I：

10.1016/j.cam.2008.04.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the convergence properties of spline collocation and iterated collocation methods for a weakly singular Volterra integral equation associated with certain heat conduction problems. This work completes the previous studies of numerical methods for this type of equations with noncompact kernel. In particular, a global convergence result is obtained and it is shown that discrete superconvergence can be achieved with the iterated collocation if the exact solution belongs to some appropriate spaces. Some numerical examples illustrate the theoretical results. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：363 / 372

页数：10

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