Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems

Abstract

This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

Keywords

• Accuracy, Block Method, Convergence, Higher-Order, Initial Value Problems (IVPs), Ordinary Differential Equations, AMS Group: 65L05, 65L06, 65L10