Bifurcations of finite difference schemes and their approximate inertial forms
- ROLF BRONSTERING, MIN CHEN
Multilevel methods are indispensable for the approximation of nonlinear evolution equations when complex physical phenomena involving the interaction of many scales are present (such as in, but without being limited to uid turbulence). Incremental unknowns of di erent types have been proposed as a means to develop such numerical schemes in the context of nite di erence discretizations. In this article, we present several numerical schemes using the so-called multilevel wavelet-like incremental unknowns. The fully discretized explicit and semi-explicit schemes for reaction-di usion equations are presented and analyzed. The stability conditions are improved when compared with the corresponding standard algorithms. Furthermore the complexity of the computation on each time step is comparable to the corresponding standard algorithm.