A new technique for solving Fredholm integro-differential equations using the reproducing kernel method

Document Type: Research Articles

Author

Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Mobarakeh, Isfahan, Iran.

Abstract

This paper is concerned with a technique for solving Fredholm integro-di erential
equations in the reproducing kernel Hilbert space. In contrast with the conventional
reproducing kernel method, the Gram-Schmidt process is omitted here
and satisfactory results are obtained. The analytical solution is represented in
the form of series. An iterative method is given to obtain the approximate solution.
The convergence analysis is established theoretically. The applicability
of the iterative method is demonstrated by testing some various examples.