Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

Additive Runge-Kutta (ARK) methods are investigated for application to the spatially discretized one-dimensional convection-diffusion-reaction (CDR) equations and results for the fifth-order method are disappointing, but both the new third- and fourth-order methods are at least as efficient as existing ARK2 methods.