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Solving Implicit Equations Arising from Adams-Moulton Methods

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Abstract

A new algorithm is given in this paper, which uses functional iteration to solve the implicit equations generated by the Adams-Moulton method. Compared with traditional function iteration, it has three advantages: (1) the center of the circle of convergence for the iteration moves to the left in hλ plane; (2) the radius of the circle is much enlarged; (3) for a fixed number of iterations, in practice, we can view it as an “explicit” method since it has a very large absolute stability region. The method is very suitable for stiff system, especially for very large systems.

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Authors and Affiliations

  1. Electric Power Research Institute Qinghe, Beijing, China, PC:100085

    Tian Min Han

  2. Core & XML group, Oracle Corp., 234 Escuela Ave. #11, Mountain View, CA, 94040, USA

    Yuhuan Han

Authors
  1. Tian Min Han
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  2. Yuhuan Han
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Han, T.M., Han, Y. Solving Implicit Equations Arising from Adams-Moulton Methods. BIT Numerical Mathematics 42, 336–350 (2002). https://doi.org/10.1023/A:1021951025649

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  • DOI: https://doi.org/10.1023/A:1021951025649

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