A note on the Rosenbrock procedure

Source 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.