Accuracy Analysis for the Solution of Initial Value Problem of ODEs Using Modified Euler Method

Abstract

There exist numerous numerical methods for solving the initial value problems of ordinary differential equations. The accuracy level and computational time are not the same for all of these methods. In this article, the Modified Euler method has been discussed for solving and finding the accurate solution of Ordinary Differential Equations using different step sizes. Approximate Results obtained by different step sizes are shown using the result analysis table. Some problems are solved by the proposed method then approximated results are shown graphically compare to the exact solution for a better understanding of the accuracy level of this method. Errors are estimated for each step and are represented graphically using Matlab Programming Language and MS Excel, which reveals that so much small step size gives better accuracy with less computational error. It is observed that this method is suitable for obtaining the accurate solution of ODEs when the taken step sizes are too much small.

Analysis of Reliable Solutions to the Boundary Value Problems by Using Shooting Method

“…Hofstrand et al [11] have discussed the bidirectional shooting method for extreme nonlinear optics. e authors have discussed some numerical methods for solving the initial value problems in [12][13][14]. Ahmad and Charan [15] make an attempt to compare the finite difference approach to the shooting method.…”