Approximate Solution of a Class of Nonlinear Volterra Integral Equations

Volume 3, Issue 3, pp 278--286 http://dx.doi.org/10.22436/jmcs.03.03.01

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Authors

Hamid Reza Erfanian - Department of Mathematics and Statistics, University of Science and Culture, Tehran, Iran Touraj Mostahsan - Department of Mathematics and Statistics, University of Science and Culture, Tehran, Iran

Abstract

In this paper we introduce an approach by an optimization method to find approximate solution for a class of nonlinear Volterra integral equations of the first and second kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

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Keywords

• Volterra integral equation
• Optimal control
• Measure theory
• Nonlinear and linear programming.

MSC

•  45G10
•  65R20
•  45B05

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