Abstract
In this article, a numerical scheme based on reproducing kernel Hilbert space method, namely multistep reproducing kernel Hilbert space method (MRKHSM), is devised to solve Chaotic and non-Chaotic systems. This algorithm is applied to Chaotic and non-Chaotic differential equations that model the Lotka-Voltera, Chen, Lorenz and Rossler systems. The numerical results demonstrate that the Multistep reproducing kernel Hilbert space method is reliable method for solving nonlinear problems.