Reproducing Kernel Hilbert Space(RKHS) method for solving singular perturbed initial value problem

Subject Areas : Applied Mathematics

Saeid Abbasbandy ^{1 *} , Mohammad Aslefallah ²

1 - Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.
2 - Department of Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran.

Received: 2016-08-24 Accepted : 2015-03-02 Published : 2016-12-01

Keywords: Reproducing Kernel Hilbert Space(RKHS), Gram-Schmidt, orthogonalization process, Singular initial value problems,

Abstract :

In this paper, a numerical scheme for solving singular initial/boundary value problems presented.By applying the reproducing kernel Hilbert space method (RKHSM) for solving these problems,this method obtained to approximated solution. Numerical examples are given to demonstrate theaccuracy of the present method. The result obtained by the method and the exact solution are foundto be in good agreement with each other and it is noted that our method is of high signicance.We compare our results with other paper. The comparison of the results with exact ones is made toconrm the validity and eciency.