Abstract
To be useful for extremely stiff systems of ordinary differential equations, A-stability and a maximally damped condition as λ h → − ∞ \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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