A Self-Starting Five-Step Eight-Order Block Method for Stiff Ordinary Differential Equations

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.