Numerical solution of third order boundary value problems using one-step hybrid block method

Abstract

Numerical hybrid block methods have been thought to be an appropriate method for solving ordinary differential equation. Therefore, this paper introduces a one-step hybrid block method of order five for directly solving third order boundary value problems. Power series of order seven is used for the development of the new method by using collocation and interpolation approach. The proposed method together with shooting technique will solve third order BVPs. Some numerical examples are involved to show the efficiency of the method. The numerical results clearly show that the developed method is able to generate good results when it is compared with existing method in terms of error. It has been noted, the new proposed method outperforms the existing methods in terms of accuracy. Subject classification: 65L06, 65L05, Keywords and phrases: Hybrid method, Block method, Third order boundary value problem, Shooting method