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

Theory of Approximation and Applications

مقاله 1، دوره 11، شماره 2، اسفند 2017، صفحه 1-14   

نوع مقاله: Research Articles

نویسنده

Razieh Ketabchi^*

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

چکیده

This paper is concerned with a technique for solving Fredholm integro-dierential
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.