Numerical Solutions of Stiff and Nonstiff Ordinary Differential Equations Using Quadratic Spline Method

Abstract

This paper deals with the numerical solution of initial value problems(IVPs), for stiff and nonstiff ordinary differential equations by  Quadratic Spline(QS) method. We convert a stiff and nonstiff equations to volterra integral equations and reduce a second order IVPs to a system of Volterra integral equations of the second kind  . The numerical results shown to verify the conclusions .A comparison of the results generated from the QS formula was carried out with some existing Runge-Kutta methods of variety of means including the Geometric Mean method, the Contraharmonic Mean method, the Centroidal Mean method, the Harmonic Mean method, the Heronian Mean method, the Root Mean Square method, and the Arithmetic Mean formula and were found to compare favourably well.  Good numerical results were obtained from the test examples and we conclude with numerical examples to justify the effectiveness of the QS method.