The Numerical Solutions for Stiff Ordinary Differential Equations by Using Interpolated Variational Iteration Method with Comparison to Exact Solutions

Abstract

Recently proposed Interpolated Variational Iteration Method (IVIM) is used to find numerical solutions of stiff ordinary differential equations for both linear and nonlinear problems. The examples are given to illustrate the accuracy and effectiveness of IVIM method and IVIM results are compared with exact results. In recent analytical approximate methods based studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method, Homotopy Analysis Method etc. In this study comparisons with exact solutions reveal that the Interpolated Variational Iteration Method (IVIM) is easy to implement. In fact, this method is promising methods for various systems of linear and nonlinear stiff ordinary differential equations as an initial value problem. Furthermore, IVIM is giving very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.