Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A LOCAL-GLOBAL STEPSIZE CONTROL FOR MULTISTEP METHODS APPLIED TO SEMI-EXPLICIT INDEX 1 DIFFERENTIAL-ALGEBRAIC EUATIONS

  • Kulikov, G.Yu (Department of Mathematics and Mechanics Ulyanovsk State university) ;
  • Shindin, S.K. (Department of Mathematics and Mechanics Ulyanovsk State university)
  • Published : 1999.09.01

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Abstract

In this paper we develop a now procedure to control stepsize for linear multistep methods applied to semi-explicit index 1 differential-algebraic equations. in contrast to the standard approach the error control mechanism presented here is based on monitoring and contolling both the local and global errors of multistep formulas. As a result such methods with the local-global stepsize control solve differential-algebraic equation with any prescribed accuracy (up to round-off errors). For implicit multistep methods we give the minimum number of both full and modified Newton iterations allowing the iterative approxima-tions to be correctly used in the procedure of the local-global stepsize control. We also discuss validity of simple iterations for high accuracy solving differential-algebraic equations. Numerical tests support the the-oretical results of the paper.

Keywords

References

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