Rosenbrock strong stability-preserving methods for convection–diffusion–reaction equations

Rosenbrock methods are normally used for solving moderately stiff problems and strong-stability preserving ones are employed a lot for hyperbolic conservation laws. Their combination called additive Rosenbrock-strong stability preserving (Ros-SSP) schemes are first introduced in this paper to deal with convection– diffusion–reaction equations. Accuracy and stability of the Ros-SSP scheme are considered. Numerical results are given to prove advantages of Ros-SSP methods. A practical application of a three-stage, second order Ros-SSP method solving a spatially discretized angiogenesis model in two-dimensional case is provided as well.