High modes smoothing of time schemes for nonlinear parabolic PDEs - Brachet, Matthieu; Chehab, Jean-Paul (Numerical algorithms, 2025)
We here introduce a stabilization process applied to IMEX time schemes for the simulation of nonlinear parabolic PDEs. The new schemes we derived use a decomposition of the signal into low and high frequency components (to which different time schemes are applied) together with a proper damping of the high mode components. This approach allows to design new methods, with enhanced stability and limited perturbation of the constituency. We display numerical analysis of the schemes on the accuracy and the stability. The numerical illustrations we give concern Allen-Cahn and Swift-Hohenberg equations, and show the efficiency of our methods. The effect of the present number of frequencies, and of the stabilization is evaluated on both the energy decay and the dynamics of the model.