A Self-Starting Five-Step Eight-Order Block Method for Stiff Ordinary Differential Equations
D. Raymond *
Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
J. Z. Donald
Department of Mathematics, Adamawa State University, Mubi, Nigeria.
A. I. Michael
Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
G. Ajileye
Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper examines the implementation of a self-starting five-step eight-order block method with two off-grid for stiff ordinary differential equations using interpolation and collocation procedures. The predictor schemes are then expanded using Taylor’s series expansion. Multiple numerical integrators were produce and arrived at a discrete scheme. The discrete schemes are of uniform order eight and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for stiff initial value problem for ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.
Keywords: Block method, stiff, five-step, power series.