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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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Linear multistep methods for stable differential equations $\ddot y=Ay+B(t)\dot y+c(t)$
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by Eckart Gekeler PDF
Math. Comp. 39 (1982), 481-490 Request permission

Abstract:

The approximation of ${y^{..}} = Ay + B(t){y^.} + c(t)$ by linear multistep methods is studied. It is supposed that the matrix A is real symmetric and negative semidefinite, that the multistep method has an interval of absolute stability $[ - s,0]$, and that ${h^2}\left \| A \right \| \leqslant s$ where h is the time step. A priori error bounds are derived which show that the exponential multiplication factor is of the form $\exp \{ {\Gamma _s}|||B|||_{n}(nh)\}$, $|||B|||_{n} = {\max _{0 \leqslant t \leqslant nh}}\left \| {B(t)} \right \|$.
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Additional Information
  • © Copyright 1982 American Mathematical Society
  • Journal: Math. Comp. 39 (1982), 481-490
  • MSC: Primary 65L05
  • DOI: https://doi.org/10.1090/S0025-5718-1982-0669641-8
  • MathSciNet review: 669641