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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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Additive Runge-Kutta methods for stiff ordinary differential equations
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by G. J. Cooper and A. Sayfy PDF
Math. Comp. 40 (1983), 207-218 Request permission

Abstract:

Certain pairs of Runge-Kutta methods may be used additively to solve a system of n differential equations $x’ = J(t)x + g(t,x)$. Pairs of methods, of order $p \leqslant 4$, where one method is semiexplicit and A-stable and the other method is explicit, are obtained. These methods require the LU factorization of one $n \times n$ matrix, and p evaluations of g, in each step. It is shown that such methods have a stability property which is similar to a stability property of perturbed linear differential equations.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Math. Comp. 40 (1983), 207-218
  • MSC: Primary 65L05
  • DOI: https://doi.org/10.1090/S0025-5718-1983-0679441-1
  • MathSciNet review: 679441