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

Subject Areas : Applied Mathematics

Razieh Ketabchi ^{1 *}

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

Received: 2015-06-22 Accepted : 2015-12-08 Published : 2017-12-01

Keywords: integro-differential equations, Reproducing kernel method, Gram-Schmidt orthogonalization process,

Abstract :

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