AN EFFICIENT ONE-EIGHT STEP HYBRID BLOCK METHOD FOR SOLVING SECOND ORDER INITIAL VALUE PROBLEMS OF ODES

E.A. Areo, M.A. Rufai

Abstract


In this article, an efficient  hybrid block method for solving second order initial value problems of ODEs was proposed. The combination of power series and exponential function were used as an approximate solution for the derivation of the methods in modified block mode. The new method is derived via interpolation and collocation approaches and the proposed method was analyzed based on the characteristics of linear multistep method and the method was found to be zero-stable, consistent, convergent and the region of absolute stability of the proposed methods of one-eight step is plotted in the figures $1$. The new proposed method gave an approximate solution to two real-life problems namely: simple harmonic motion and critically damped motion problems. Six numerical examples were solved to determine the efficiency and accuracy of the new method and the numerical solutions obtained yielded  better results when compared with some existing methods in the literature.

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