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A Special Family of LMM with Two Hybrid Points for Stiff ODEs
Abstract
Hybrid methods with one or more off-step points give better stability
characteristics and higher order than the conventional linear multistep methods (LMM). Enright (1974) discussed the formulation of the second derivative LMM which was found to be stiffly stable for step number k £ 7 for the numerical solution of stiff Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs). In this paper some second derivative continuous linear multistep methods with two hybrid points are proposed for step number k £ 9 for stiff ODEs. The derivation of these methods is based on collocation and interpolation approach of Onumanyi et al (1996)
and Arevalo et al (2002). The family of methods is stiffly stable for k £ 8 and of comparable accuracy to the Enright’s method and the state of-the-art code Ode 15s in MATLAB.
Keywords: , Hybrid points, Continuous LMM, stiffly stable.
characteristics and higher order than the conventional linear multistep methods (LMM). Enright (1974) discussed the formulation of the second derivative LMM which was found to be stiffly stable for step number k £ 7 for the numerical solution of stiff Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs). In this paper some second derivative continuous linear multistep methods with two hybrid points are proposed for step number k £ 9 for stiff ODEs. The derivation of these methods is based on collocation and interpolation approach of Onumanyi et al (1996)
and Arevalo et al (2002). The family of methods is stiffly stable for k £ 8 and of comparable accuracy to the Enright’s method and the state of-the-art code Ode 15s in MATLAB.
Keywords: , Hybrid points, Continuous LMM, stiffly stable.
