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Mathematics of Computation

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A note on the Rosenbrock procedure


Author: T. D. Bui
Journal: Math. Comp. 33 (1979), 971-975
MSC: Primary 65L05
DOI: https://doi.org/10.1090/S0025-5718-1979-0528050-2
MathSciNet review: 528050
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Abstract: To be useful for extremely stiff systems of ordinary differential equations, A-stability and a maximally damped condition as $ \lambda h \to - \infty $ (i.e., L-stability) are desirable. This paper investigates the condition of L-stability for a class of Runge-Kutta methods known as the Rosenbrock procedure. This procedure requires only one computation of a Jacobian matrix per step of integration, L-stable Rosenbrock methods up to order four are derived.


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DOI: https://doi.org/10.1090/S0025-5718-1979-0528050-2
Article copyright: © Copyright 1979 American Mathematical Society