A One-Step Hybrid Obrechkoff-Type Block Method for First-Order Initial Value Problems in Ordinary Differential Equations

Abstract

In this paper, we propose a one-step hybrid block method of the Obrechkoff-type block method for solving initial value problems in ordinary differential equations using Taylor series expansion. The new method was implemented with some selected initial value problems to determine the efficiency and accuracy of the method. The convergence and stability properties were also examined. It was discovered that the new method compared favorably with other existing methods in the selected literature.