An Accurate Implicit Quarter Step First Derivative Block Hybrid Method (AIQSFDBHM) for Solving Ordinary Differential Equations

Abstract

The new accurate implicit quarter step first derivative blocks hybrid method for solving ordinary differential equations have been proposed in this paper via interpolation and collocation method for the solution of stiff ODEs. The analysis of the method was study and it was found to be consistent, convergent, zero-stability, We further compute the region of absolute stability region and it was found to be Aα − stable . It is obvious that, the numerical experiments considered showed that the methods compete favorably with existing ones. Thus, the pair of numerical methods developed in this research is computationally reliable in solving first order initial value problems, as the results from numerical solutions of stiff ODEs shows that this method is superior and best to solve such problems as in tables and figures.

Three-step Four-point Optimized Hybrid Block Method for Direct Solution of General Third Order Differential Equations

“…Lambert [1][2] discussed extensively the approach of reducing higher order ODEs to system of lower order, specifically first order equations and then applying various methods available for solving the resulting system of first order IVPs. The direct solution of higher order numerically without reducing to a system of first order initial value problems have been studied by various authors such as Mohammed and [3][4][5][6][7]. Kuboye and Omar [8] proposed seven-step block method for solving third order ODEs.…”