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Constant coefficient linear multistep methods with step density control

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Author

Summary, in English

In linear multistep methods with variable step size, the method's coefficients are functions of the step size ratios. The coefficients therefore need to be recomputed on every step to retain the method's proper order of convergence. An alternative approach is to use step density control to make the method adaptive. If the step size sequence is smooth, the method can use constant coefficients without losing its order of convergence. The paper introduces this new adaptive technique and demonstrates its feasibility with a few test problems. The technique works in perfect agreement with theory for a given step density function. For practical use, however, the density must be generated with data computed from the numerical solution. We introduce a local error tracking controller, which automatically adapts the density to computed data, and demonstrate in computational experiments that the technique works well at least up to fourth-order methods. (c) 2006 Elsevier B.V. All rights reserved.

Department/s

Publishing year

2007

Language

English

Pages

891-900

Publication/Series

Journal of Computational and Applied Mathematics

Volume

205

Issue

2

Document type

Journal article

Publisher

Elsevier

Topic

  • Mathematics

Keywords

  • density control
  • non-uniform grid
  • step
  • step size selection
  • multistep method
  • variable step size method

Status

Published

Research group

  • Numerical Analysis

ISBN/ISSN/Other

  • ISSN: 0377-0427