Numerical Solutions of a Class of Nonlinear Volterra Integral Equations

被引：1
|
作者：
Malindzisa, H. S. [1 ]
Khumalo, M. [1 ]
机构：
[1] Univ Johannesburg, Dept Pure & Appl Math, ZA-2006 Auckland Pk, South Africa
来源：
ABSTRACT AND APPLIED ANALYSIS | 2014年
关键词：
ITERATED COLLOCATION METHODS; 2ND KIND;
D O I：
10.1155/2014/652631
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider numerical solutions of a class of nonlinear (nonstandard) Volterra integral equations. We first prove the existence and uniqueness of the solution of the Volterra integral equation in the context of the space of continuous functions over a closed interval. We then use one-point collocation methods with a uniform mesh to construct solutions of the nonlinear (nonstandard) VIE and quadrature rules. We conclude that the repeated Simpson's rule gives better solutions when a reasonably large value of the stepsize is used.
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页数：8
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