Open Access
2014 Numerical Solutions of a Class of Nonlinear Volterra Integral Equations
H. S. Malindzisa, M. Khumalo
Abstr. Appl. Anal. 2014: 1-8 (2014). DOI: 10.1155/2014/652631


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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H. S. Malindzisa. M. Khumalo. "Numerical Solutions of a Class of Nonlinear Volterra Integral Equations." Abstr. Appl. Anal. 2014 1 - 8, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022831
MathSciNet: MR3232855
Digital Object Identifier: 10.1155/2014/652631

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
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