A new analytical method for solving systems of Volterra integral equations

Abstract

In this paper, a new modified homotopy perturbation method (NHPM) is introduced for solving systems of Volterra integral equations of the second kind. Theorems of existence and uniqueness of the solutions to these equations are presented. Comparison of the results of applying the NHPM with those of the homotopy perturbation method and Adomian's decomposition method leads to significant consequences. Several examples, including the system of linear and nonlinear Volterra integral equations, are given to demonstrate the efficiency of the new method.

Keywords:

• system of Volterra integral equations
• homotopy perturbation method
• existence
• uniqueness
• NHPM

2000 AMS Subject Classifications::

• 45D05
• 45L05
• 45G15

Acknowledgements

The author would like to thank both referees for their comments that improved the presentation of the paper.