MULTILEVEL CORRECTION FOR COLLOCATION SOLUTIONS OF VOLTERRA NONL INEARINTEGRO-DIFFERENTIAL EQUATIONS

作     者：HU Qiya (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) PENG Long (School of 

作者机构：中科院计算数学与科学工程计算所 北京 100080 北京外国语大学国际商学院 北京 100081 

出 版 物：《Systems Science and Mathematical Sciences》 (SYSTEMS SCIENCE AND MATHEMATICAL SCIENCES)

年 卷 期：2000年第13卷第2期

页      面：170-180页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：This research is supported by the National Natural Science Foundation of China!19801030 

主　　题：Nonlinear integro-differential equation collocation solution error expansion multilevel correction. 

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 h2m. 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)).