The reproducing kernel Hilbert space method for solving Troesch’s problem

Abstract

In this paper, the reproducing kernel Hilbert space method (RKHSM) is applied for solving Troesch’s problem. We used numerical examples to illustrate the accuracy and implementation of the method. The analytical result of the equation has been obtained in terms of a convergent series with easily computable components. The results are compared with the ones obtained by the homotopy perturbation method (HPM), the Laplace decomposition method (LDM), the perturbation method (PM), the Adomian decomposition method (ADM), the variational iteration method (VIM), the B-spline method and the nonstandard finite difference scheme (FDS) by using tables and figures. Numerical results show that the present method is effective.