A ninth-order first derivative method for numerical integration

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In this paper, we present a ninth–order block hybrid method for the numerical solution of stiff and non–stiff systems of first–order differential equations. The method is based on an interpolation and collocation approach which results in a single continuous formulation; from which eight discrete schemes that make the block method were obtained. A convergence analysis of our method illustrated that it is A–stable, consistent, and convergent. We applied our method to some numerical examples which showed that the new method not only outperformed a second derivative method of order fourteen in the literature but also compared well with the exact solution.

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