The computation of numerical method second derivative for the direct solution of higher order initial value problems

Abstract

We have proposed the computation of numerical method second derivative for the direct solution of higher order Initial Value Problems (IVPs) on implicit one step block method in this research. The method was derived via interpolation and collocation procedure by introduction of off-mesh point at both grid and off-grid, using the power series. The analysis of the method was examined, and it was found to be consistent, zero-stable and convergent. The new method is tested on some highly stiff
problems without reduction to the equivalents system of first order ordinary differential equations (ODEs). And our method performs better when compared with the existing methods in terms of accuracy. We further sketched the solution graph of our method and it is obvious that the new method converges toward the exact solution.