On the Application of the Block Hybrid Methods to Solve Linear and Non-Linear First Order Differential Equations

Abstract

Block hybrid methods with intra-step points are considered in this study. These methods are implemented to solve linear and nonlinear single and systems of first order differential equations. The stability, convergence, and accuracy of the proposed methods are qualitatively investigated through the absolute and residual error analysis in some selected cases. A number of different numerical examples are tested to demonstrate the efficiency and applicability of the proposed methods. In this study we also implement the proposed methods to solve chaotic systems such as the Glukhvsky–Dolzhansky system, producing very comparable results to those already in the literature.