A Modified ODE Solver for Autonomous Initial Value Problems

Abstract

In this work, modified version of a well-known variant of Euler method, known as the Improved Euler method,is proposed with a view to attain greater accuracy and efficiency. The attention is focused upon performance ofthe proposed method in autonomous initial value problems of ordinary differential equations. Order of accuracyof the proposed modified method is proved to be two using Taylor’s expansion. Numerical experiments areperformed using MS Excel 2010.Keywords: ODE solver, numerical solution, initial value problem.