Development and analysis of fifth stage inverse polynomial scheme for the solution of stiff linear and nonlinear ordinary differential equations

Abstract

This paper presents the development and analysis of fifth stage inverse polynomial scheme (ISM5) for the solution of Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) of stiff types. The properties of the scheme were investigated and analyzed. The new scheme is tested on three numerical examples and the results were compared with the Runge-Kutta method of order five (RK5) in the context of the analytical solution. The results generated via ISM5 agreed with the analytical solution and outperformed RK5. Hence, ISM5 is found to be accurate, efficient and a powerful method for obtaining the numerical solution of stiff ODEs.