A new reproducing kernel method for solving Volterra integro-dierential equations

Theory of Approximation and Applications

دوره 13، شماره 2، اسفند 2019، صفحه 1-17

نوع مقاله: Research Articles

نویسنده

Razieh Ketabchi^*

Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Esfahan, Iran

چکیده

This paper is concerned with a technique for solving Volterra 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.

کلیدواژه‌ها

Reproducing kernel method؛ integro-differential equations؛ Gram-Schmidt orthogonalization process