On Local Error Bound of a Modified Ordinary Differential Equation Solver

Abstract

In this paper, a second order accurate numerical method for the solution of Ordinary Differential Equations (ODEs) referred to as the Modified ODE Solver (Memon et al., 2014) is analyzed on the basis of bounds on local truncation error and step size. The error and step size bounds for the modified ODE solver have been formulated by following the approach of Lotkin (1951) and are compared to those of second order accurate Improved Euler (IE) and Improved Modified Euler (IME) methods. The Modified ODE Solver is found to have the minimum local error bound and the maximum step size bound with the help of supporting numerical examples.