4-STEP HYBRID METHODS FOR SOLVING SECOND ORDER INITIAL VALUE ORDINARY DIFFERENTIAL EQUATIONS

Abstract

In this research, 4-step hybrid methods for solving second order initial value ordinary differential equations are developed with the use of Chebychev polynomial of first kind as the basis function. The approach is based on collocation of differential system at selected grid points and interpolation of basis function at all grid points except at the evaluation point. The resulting system of operation is solved for the unknown parameters and these values were substituted in to the approximate solution to obtain the main scheme and the additional scheme to solve Ordinary Differential Equations (ODEs). The predictors for the evaluation of the main schemes are obtained to be of the same order with the corrector. The derived methods were tested for consistency, stability and convergence, the method was implemented by using it to solve test problem. Accuracy of the methods were compared with predictor corrector and block methods.