A note on the Rosenbrock procedure

Author:
T. D. Bui

Journal:
Math. Comp. **33** (1979), 971-975

MSC:
Primary 65L05

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 (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