Construction of Five-step Continuous Block General Method for the Solution of 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.
J. A. Oladunjoye
Department of Compuer Science, Federal University Wukari, Taraba State, Nigeria.
A. Lydia
Department of Mathematics and Statistics, Federal University Wukari, Taraba State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, a self starting five step Continuous Block Hybrid Adams Moulton Method (CBHAM) with three off-grid points is developed using collocation and interpolation procedures. The predictor schemes are then expanded using Taylor’s series expansion. Multiple numerical integrators were produced and arrived at some discrete schemes. The discrete schemes are of uniform order and are assembled into a single block matrix equation. These equations are simultaneously applied to provide the approximate solution for stiff initial value problems for ordinary differential equations. The order of accuracy and stability of the block method is discussed and its accuracy is established numerically.
Keywords: Block general method, stiff, five-step, power series, continuous