Accurate and Efficient Implementation of Block Hybrid Method for Solving Special Second Order Ordinary Differential Equations

Abstract

In this paper, linear multistep technique using power series as the basis function is used to develop a block method which is suitable for generating direct solution of the special second order ordinary differential equations of the form ( equation available in paper due to mathematical expressions.) with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Further more, a stability analysis and efficiency of the block method are tested on linear and non-linear ordinary differential equations whose solutions are oscillatory or nearly periodic in nature, and the results obtained compared favourably with the exact solution.