Modified Milne’s Method for Solving IVP Using Matlab

Abstract

The solution of an initial value problem in ordinary differential
equations expanded as Milne’s method has been given as both a
classical and a numerical method. In this paper, we first describe
methods for solving initial value problems and then explain the Milne’s
method. When considering the numerical solution of ordinary
differential equations (ODEs), a predictor–corrector method typically
uses an explicit method for the predictor step and an implicit method
for the corrector step. Our aims are proposing a modified form of the
Milne’s Predictor-Corrector formula for solving ordinary differential
equation of first order and first degree. We followed the applied
mathematical method numerically by MATLAB. We found that Milne’s
(modified) predictor-corrector formula gives better accuracy and it
also can minimize the calculating time as it takes less number of
iterations. In addition, toits a multi-step method to compute y for
preceding values of y and y′ is essentially required.