New efficient time integrators for non-linear parabolic problems

Abstract

In this work a new numerical method is constructed for time-integrating multidimensional parabolic semilinear problems in a very efficient way. The method reaches the fourth order in time and it can be combined with standard spatial discretizations of any order to obtain unconditinally convergent numerical algorithms. The main theoretical results which guarantee this property are explained here, as well as the method characteristics which guarantee a very strong reduction of computational cost in comparison with classical discretization methods.