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

Document Type: Research Articles

Authors

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

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 the
accuracy of the present method. The result obtained by the method and the exact solution are found
to 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 to
con rm the validity and eciency.

[1] S. Abbasbandy, B. Azarnavid, M.S. Alhuthali, A shooting reproducing
kernel Hilbert space method for multiple solutions of nonlinear boundary
value problems,Journal of Computational and Applied Mathematics, 279
(2015), 293-305.
[2] S. Abbasbandy, B. Azarnavid, Some error estimates for the reproducing
kernel Hilbert spaces method, Journal of Computational and Applied
Mathematics, 296 (2016) 789-797.
[3] B. Azarnavid, F. Parvaneh, S. Abbasbandy, Picard-Reproducing Kernel
Hilbert Space Method for Solving Generalized Singular Nonlinear Lane-
Emden Type Equations, Mathematical Modelling and Analysis, 20(6)
(2015) 754-767.
[4] M. Cui, Y. Lin, Nonlinear numerical analysis in the reproducing kernel
space, Nova Science Pub. Inc., Hauppauge, 2009.
[5] Ghazala Akram, Hamood Ur Rehman, Solution of First Order Singularly
Perturbed Initial Value Problem in Reproducing Kernel Hilbert Space,
European Journal of Scienti c Research, 53(4) (2011) 516-523.
[6] S. Gh. Hosseini, S. Abbasbandy, Solution of Lane-Emden Type Equations
by Combination of the Spectral Method and Adomian Decomposition
Method, Mathematical Problems in Engineering, Vol. 2015, Article ID
534754, 10 pages, 2015.
[7] S. Iqbal, A. Javed , Application of optimal homotopy asymptotic method
for the analytic solution of singular Lane-Emden type equation, Applied
Mathematics and Computation, 217 (2011) 7753-7761.