Second Derivatives Single Step Block Hybrid Method for Non-Linear Dynamical System

In this paper, a modified single-step method is proposed to integrate nonlinear dynamical systems resulting to ordinary differential equations. In order to obtain higher order A-stable method, we have used second derivative of the solutions and imposed some special sets of off-grid points in the formulation process of the algorithms. The consistency, convergence and order of accuracy of the algorithms were successfully established and in addition, the method is found to be A-stable. The proposed method which is self-starting were applied as simultaneous numerical integrators on non-overlapping intervals. In order to demonstrate the effectiveness of the proposed algorithms, some nonlinear dynamical systems of IVPs with applications in population growth models, chaos and vibratory theory are considered. and results obtained are compared with those from related schemes and from other methods in the literature.