Abstract and Applied Analysis

Numerical Solutions of a Class of Nonlinear Volterra Integral Equations

H. S. Malindzisa and M. Khumalo

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 652631, 8 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412277101

Digital Object Identifier
doi:10.1155/2014/652631

Mathematical Reviews number (MathSciNet)
MR3232855

Zentralblatt MATH identifier
07022831

Citation

Malindzisa, H. S.; Khumalo, M. Numerical Solutions of a Class of Nonlinear Volterra Integral Equations. Abstr. Appl. Anal. 2014 (2014), Article ID 652631, 8 pages. doi:10.1155/2014/652631. https://projecteuclid.org/euclid.aaa/1412277101


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