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Multistep methods for differential algebraic equations

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Abstract

Multistep methods for the differential/algebraic equations (DAEs) in the form of

$$F_1 (x) = 0, F_2 (x,x',z) = 0$$

are presented, whereF 1 maps from ℝn to ℝ′,F 2 from ℝn x ℝn x ℝm to ℝs andr<n≤r+s=n+m. By employing the deviations of the available existence theories, a new form of the multistep method for solutions of (1) is developed. Furthermore, it is shown that this method has no typical instabilities such as those that may occur in the application of multistep method to DAEs in the traditional manner. A proof of the solvability of the multistep system is provided, and an iterative method is developed for solving these nonlinear algebraic equations. Moreover, a proof of the convergence of this iterative method is presented.

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Authors and Affiliations

  1. Institute of Computational Mathematics and Applications, Department of Mathematics and Statistics, University of Pittsburgh, 15260, Pittsburgh, PA, USA

    Xiaopu Yan

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  1. Xiaopu Yan
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Communicated by C. Brezinski

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Yan, X. Multistep methods for differential algebraic equations. Numer Algor 10, 245–260 (1995). https://doi.org/10.1007/BF02140771

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  • DOI: https://doi.org/10.1007/BF02140771

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