Abstract

THE USE OF LINEAR MULTISTEP METHOD ON IMPLICIT ONE-STEP SECOND DERIVATIVE BLOCK METHOD FOR DIRECT SOLUTION OF HIGHER ORDER INITIAL VALUE PROBLEMS

Donald, J. Z.,1 Skwame, Y.,1 Sabo, J.1 and Ayinde, A. M.2

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The derivation of implicit one-step second derivative block method using power series for direct solution of higher order initial value problems have been developed in this research. The method was derived using interpolation and collocation procedure by introduction of off-mesh point at both grid and off-grid on linear multistep method. The analysis of the method was examined, and it was found to be consistent, zero-stable and convergent. The newly derived method was able to solve some highly stiff problems. The generated results, showed that the derived methods are notable better than those methods in literature. It is evident that, this research has helped researchers, students in area of science, engineering and social science. Keywords: Block Method, Implicit One-step, Initial Value Problems, Interpolation and Collocation, Linear Multistep Method, Power Series, Second Order.

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