ABSTRACT
A family of A-stable generalized hybrid multistep methods that preserves the equilibrium solution of ordinary differential equations is presented for the solution of stiff differential equations. In deriving the algorithms, off-step grid points are incorporated, the resultant methods are then transformed into generalized linear multistep methods. The interval of stability are investigated and the boundary locus points are given in the figure; the stability region of the developed methods is the exterior of the closed curves. Numerical experiments are performed to demonstrate the accuracy of the method. The derived methods are implemented on Kepler’s and chemical reaction problems. The result shows that the Generalized Hybrid Multistep methods are adequate and suitable for solving Stiff Ordinary Differential Equations.
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