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Hybrid Extended Backward Differentiation Formulas for Stiff Systems

Ali K. Ezzeddine, Gholamreza Hojjati

Open publisher page 5 citations

Abstract

In this paper we present details of a new class of hybrid methods which are based on backward differentiation formula (BDF) for the numerical solution of ordinary differential equations. In these methods, the first derivative of the solution in one super future point as well as in one off-step point is used to improve the absolute stability regions. The constructed methods are A( )-stable up to order 9 so that, as it is shown in the numerical experiments, they are superior for stiff systems.

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What this paper is about

In this paper we present details of a new class of hybrid methods which are based on backward differentiation formula (BDF) for the numerical solution of ordinary differential equations. In these methods, the first derivative of the solution in one super future point as well as in one off-step point is used to improve the absolute stability regions. The constructed methods are A( )-stable up to order 9 so that, as it is shown in the numerical experiments, they are superior for stiff systems.

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OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper we present details of a new class of hybrid methods which are based on backward differentiation formula (BDF) for the numerical solution of ordinary differential equations. In these methods, the first derivative of the solution in one super future point as well as in one off-step point is used to improve the absolute stability regions. The constructed methods are A( )-stable up to order 9 so that, as it is shown in the numerical experiments, they are superior for stiff systems.

Key concepts: Backward differentiation formula, Numerical differentiation, Mathematics, Linear multistep method, Ordinary differential equation, Stability (learning theory), Numerical analysis, Numerical methods for ordinary differential equations

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