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1991•SIAM Journal on Numerical AnalysisRequires access

Approximation Methods for the Consistent Initialization of Differential-Algebraic Equations

Benedict Leimkuhler, Linda Petzold, C. W. Gear

Open publisher page 96 citations

Abstract

The algebraic constraints in a system of differential-algebraic equations (DAEs) impose a consistency requirement on the initial values that can be difficult to satisfy. In this paper the consistency requirement is characterized by a system of equations. An approximation method is introduced for these equations, and the numerical solution of the resulting system is analyzed for certain important classes of DAEs. Finally, a numerical experiment is described.

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What this paper is about

The algebraic constraints in a system of differential-algebraic equations (DAEs) impose a consistency requirement on the initial values that can be difficult to satisfy. In this paper the consistency requirement is characterized by a system of equations. An approximation method is introduced for these equations, and the numerical solution of the resulting system is analyzed for certain important classes of DAEs. Finally, a numerical experiment is described.

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OpenAlex reports 96 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The algebraic constraints in a system of differential-algebraic equations (DAEs) impose a consistency requirement on the initial values that can be difficult to satisfy. In this paper the consistency requirement is characterized by a system of equations. An approximation method is introduced for these equations, and the numerical solution of the resulting system is analyzed for certain important classes of DAEs. Finally, a numerical experiment is described.

Key concepts: Mathematics, Differential algebraic equation, Initialization, Consistency (knowledge bases), Algebraic equation, Differential algebraic geometry, Algebraic number, Applied mathematics

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