Modified parallel Rosenbrock methods for stiff differential equations

To raise the efficiency of Rosenbrock methods Chen Lirong and Liu Degui have constructed the parallel Rosenbrock methods in 1995, which are written as PRMs for short. In this paper we present a class of modified parallel Rosenbrock methods which possesses more free parameters to improve further the various properties of the methods and will be similarly written as MPROWs, Convergence and stability of MPROWs are discussed. Especially, by choosing free parameters appropriately, we search out the practically optimal 2-stage 3rd-order and 3-stage 4th-order MPROWs, which are all A-stable and have small error constants. Theoretical analysis and numerical experiments show that for solving stiff problems the MPROWs searched out in the present paper are much more efficient than the existing parallel and sequential methods of the same type and same order mentioned above.