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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Marginal stability and stabilization in the numerical integration of ordinary differential equations
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by H. Brunner PDF
Math. Comp. 24 (1970), 635-646 Request permission

Abstract:

Strongly stable and consistent multistep methods with maximum order are subject to marginal (or weak) stability. In this paper we introduce modified multistep methods whose coefficients depend linearly on the stepsize $h$ and a parameter $L$ in such a way that the order of the original method is not decreased. By choosing $L$ in a suitable manner (depending essentially on ${f_y}(x,y)$ of the differential equation $y’ = f(x,y)$ and on the growth parameters of the multistep method), marginal stability can be eliminated.
References
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 635-646
  • MSC: Primary 65.61
  • DOI: https://doi.org/10.1090/S0025-5718-1970-0273821-5
  • MathSciNet review: 0273821