Moving mesh method with local time step refinement for blow-up problems

摘要

In this paper, the dynamical moving mesh method is merged with the local time stepping technique and the new method is applied for blow-up problems. It has some benefit in approximating an accurate blow-up time by starting at any positive initial time (t0 > 0).Our numerical experiment shows that without applying the local time stepping method, wrong blow-up time will be obtained, if the equation integrates from t0 > 0.