Fourth-order parallel rosenbrock formulae for stiff systems

K e y w o r d s R o s e n b r o c k methods, A-stable, Parallel algorithm, Stiff initial value problem, Adal> tivity. 1. I N T R O D U C T I O N We consider the numerical solution of systems of initial value ordinary differential equations (ODEs), i.e., initial value problems (IVPs), of the form y'(t) -f (y(t)) , y(to) = Yo, (1) where y : R --* R "~ and f : R "~ --* R m. Runge-Kutta methods applied to stiff systems of form (1) must necessarily be implicit due to stability constraints on the step size, but ultimately necessitate significant computational effort due to their iterative nature. Linearly implicit methods, such as Rosenbrock methods [1], have already proven very effective at low to modest accuracies for a wide variety of stiff problems [2]. Moreover, they are noniterative in design which is an asset for parallel implementation as true iteration may create load imbalancing in a parallel implementation [3,4]. When applied to (1), an s-stage Rosenbrock method has the form [5,6]