Efficient Seventh-Order Hybrid Block Process for Solving Stiff Second Order Ordinary Differential Equationsl.

Abstract

In this research, we proposed a derivation and application of an accurate hybrid block method for the direct integration of second order ordinary differential equations with initial value problems. The method developed by way of collocating and interpolating the 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 basic properties such as order, error constant, zero stability, consistency and convergence of the method were properly examined. The block method derived produces more efficient results when compared with the work carried out by some authors to solve stiff second order ordinary differential equations. Keywords: Power Series, Collocation and Interpolation, Block Method, Initial Value Problems, and Stiff ODEs