Splitting methods for constrained diffusion-reaction systems

摘要

We consider Lie and Strang splitting for the time integration of constrainedpartial differential equations with a nonlinear reaction term. Since suchsystems are known to be sensitive with respect to perturbations, the splittingprocedure seems promising as we can treat the nonlinearity separately. This hassome computational advantages, since we only have to solve a linear constrainedsystem and a nonlinear ODE. However, Strang splitting suffers from orderreduction which limits its efficiency. This is caused by the fact that thenonlinear subsystem produces inconsistent initial values for the constrainedsubsystem. The incorporation of an additional correction term resolves thisproblem without increasing the computational cost. Numerical examples includinga coupled mechanical system illustrate the proven convergence results.