Numerical Technique via Interpolating Function for Solving Second Order Ordinary Differential Equations

Fadugba SE

Published on: 2019-05-28

Abstract

In this research paper, a third order convergent numerical method is proposed for the solution of the initial value problem of second order ordinary differential equations has been investigated for its stability region and accuracy. The method has been recently devised via interpolating function consisting of both exponential and polynomial functions. Illustrative examples have been solved numerically to test the performance, accuracy of the proposed method in the context of the exact solution and Euler method in terms of the absolute errors computed at each nodal point of the associated integration interval. The numerical results show that the method performs excellently and agrees perfectly with the exact values. It is also observed that as the computation progresses, there is no significant difference between the values of the proposed method and that of the exact solution unlike its counterpart the Euler’s method. Hence, this third order convergent method is a good tool for the solution of second order initial value problem in ordinary differential equations. All calculations have been carried out via MATLAB (R2014a) in double precision.