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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Embedded diagonally implicit Runge-Kutta algorithms on parallel computers
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by P. J. van der Houwen, B. P. Sommeijer and W. Couzy PDF
Math. Comp. 58 (1992), 135-159 Request permission

Abstract:

This paper investigates diagonally implicit Runge-Kutta methods in which the implicit relations can be solved in parallel and are singly diagonal-implicit on each processor. The algorithms are based on diagonally implicit iteration of fully implicit Runge-Kutta methods of high order. The iteration scheme is chosen in such a way that the resulting algorithm is $A(\alpha )$-stable or $L(\alpha )$-stable with $\alpha$ equal or very close to $\pi /2$. In this way, highly stable, singly diagonal-implicit Runge-Kutta methods of orders up to 10 can be constructed. Because of the iterative nature of the methods, embedded formulas of lower orders are automatically available, allowing a strategy for step and order variation.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 135-159
  • MSC: Primary 65L06; Secondary 65Y05
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1106986-8
  • MathSciNet review: 1106986