New Continuous Hybrid Constant Block Method for the Solution of Third Order Initial Value Problem of Ordinary Differential Equations

In this study, a new one step continuous hybrid constant block method is developed using interpolation and collocation of power series approximate solution to solve initial -value problems involving third -order ordinary differential equations. The one step block method was augmented by the introduction of off grid points so as to circumvent Dahquist zero stability barrier. The block method is then applied to obtain the solution of two numerical examples for demonstration of the efficiency of the new method. The results are compared with the existing ones in literature and it is concluded that results of Continuous Hybrid Constant Block Method is more accurate than when it was implemented in predictor corrector mode or using implicit Runge-Kutta method.