An Accurate Implicit Quarter Step First Derivative Block Hybrid Method (AIQSFDBHM) for Solving Ordinary Differential Equations
P. Tumba
Department of Mathematics, Federal University, Gashua, Nigeria.
J. Sabo *
Department of Mathematics, Adamawa State University, Mubi, Nigeria.
A. A. Okeke
Department of Mathematics, Federal University, Gashua, Nigeria.
D. I. Yakoko
Department of Mathematics and Statistics, Taraba State Polytechnic, Suntai, Jalingo Campus, Nigeria.
*Author to whom correspondence should be addressed.
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.
Keywords: Quarter-step, block hybrid, first derivative.