Time discretization/linearization approach based on HOC difference schemes for semilinear parabolic systems of atmosphere modelling

Abstract

We implement implicit-explicit (IMEX) linear multistep time-discretization to HOC difference schemes for weakly coupled nonlinear parabolic systems with desirable time-step restrictions and positivity preservation of the numerical solution. Numerical experiments are performed with IMEX-BDF1 (backward difference method of order one), IMEX-BDF2 (backward difference method of order two) and CN-LF (Crank-Nicolson Leap Frog) to check the properties of the methods.