Numerical Solution of a Non-Linear Volterra Integral Equation

被引：9
|
作者：
Maleknejad K. [1 ]
Torabi P. [2 ]
Sauter S. [3 ]
机构：
[1] School of Mathematics, Iran University of Science, Technology, Narmak, 16846 13114, Tehran
[2] Department of Basic Sciences, Jundi-Shapur University of Technology, Dezful
[3] Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, Zürich
来源：
Vietnam Journal of Mathematics | 2016年 / 44卷 / 1期
关键词：
Adaptive quadrature; Fixed point method; Fixed point theorem; Measure of noncompactness; Nonlinear quadratic Volterra integral equation; Nonuniform interpolation nodes;
D O I：
10.1007/s10013-015-0149-8
中图分类号：
学科分类号：
摘要：
In this paper, a numerical method to solve non-linear integral equations based on a successive approximation technique is considered. A sequence of functions is produced which converges to the solution. The process includes a fixed point method, a quadrature rule, and an interpolation method. To find a total bound of the error, we investigate error bounds for each approximation and by combining them, we will derive an estimate for the total error. The accuracy and efficiency of the method is illustrated in some numerical examples. © 2015, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.
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页码：5 / 28
页数：23
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