Hybrid block predictor-hybrid block corrector for the solution of first-order ordinary differential equations

Abstract

This paper considers the development of one step four, hybrid block method for the solution of first order initial value problems of ordinary differential equations. The method was developed by collocation and interpolation of power series approximate solution to generate a continuous implicit linear multistep method. Both the predictor and corrector are implemented in block method. The basic properties of the derived method are investigated and found to be convergent and the efficiency was tested on some numerical examples and found to give better approximation than the existing methods.