Approximate solution of a system of linear integral equations by the Taylor expansion method

Abstract

A simple and efficient approximate technique is developed to obtain the solution to a system of linear integral equations. This technique is based on the Taylor expansion. The method has been successfully applied to determine approximate solutions of a system of Fredholm integral equations and Volterra integral equations of not only the second kind but also the first kind. The mth order approximation of the solution is exact up to a polynomial of degree equal to or less than m. Several illustrative examples are presented to show the effectiveness and accuracy of this method.

Keywords:

• approximate solution
• Taylor expansion
• Fredholm integral equations
• Volterra integral equations
• linear equations

Mathematics Subject Classifications :

• 45F05
• 65R20
• 45B05

Acknowledgements

The work was supported partially by the National Natural Science Foundation of China under Grant No. 10672189.