On Consistency, Stability and Convergence of a Modified Ordinary Differential Equation Solver

Abstract

In this piece of work, a Modified Ordinary Differential Equation Solver, proposed for the numerical solution of initial value problems in ordinary differential equations is analyzed on the basis of consistency, stability and convergence - characteristics essential for a numerical method to be of any use. A comparison is made between the regions of absolute stability of the Improved Euler method and the Modified Ordinary Differential Equation Solver; the later having the same order of accuracy as the former, possesses a larger stability region