MULTILEVEL CORRECTION FOR COLLOCATION SOLUTIONS OF VOLTERRA NONLINEAR INTEGRO-DIFFERENTIAL EQUATIONS

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外文摘要：In this paper we give a complete analysis of the convergence acceleration method for collocation solutions of Volterra nonlinear integro-differential equations with smooth kernels. It will be shown that when continuous piecewise polynomials of degree m are used and collocation is based on the Lobatto points, the first derivative of this collocation approximation admits, at the knots, an error expansion in even powers of the step-size h, beginning with a term in h2n. On the basis of this expansion we show that when a correction procedure is applied to this collocation approximation for k times, the global accurary of the corresponding corrected approximation will be increased to O(h2m(k+1)).

外文关键词：

Nonlinear integro-ditterential equationcollocation solutionerror expansionmultilevel correction

作者：

HU Qiya、PENG Long

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作者单位：

Institute of Computational Mathematics and Scientific/Engineering Computing,Chinese Academy of Sciences, Beijing 100080；Institute for Computing Mathematics and Applied Mathematics, Xiangtan University, Hunan 411105, China

School of International Business, Beijing Foreign Studies University, Beijing 100081, China

基金：

国家自然科学基金

项目编号：

19801030

出版年：

2000

系统科学与复杂性学报(英文版)

中国科学院系统科学研究所

系统科学与复杂性学报(英文版)

CSCD

影响因子：0.181

ISSN：1009-6124

年,卷(期)：2000.13(2)