Seventh-Order Hybrid Block Algorithm for Direct Solution of Stiff Second Order Ordinary Differential Equations

Abstract

Presented in this article is the derivation and application of an accurate hybrid block method for the direct computational solution of second order ordinary differential equations with initial value problems. The scheme was developed via collocation and interpolation of power series approximation to give a continuous linear multistep method. The evaluation of the continuous method at the grid and off grid points produced the discrete block method. The order, error constant, zero stability, consistency and convergence of the method were properly examined.  The new block method generated more accurate result when compared with the work carried out by existing authors on the solution of stiff second order ordinary differential equations. The new method is therefore recommended for the solution of stiff second order ordinary differential equations. MAPPLE software was used for the computation.