Efficient adaptive step size control for exponential integrators

Traditional step size controllers make the tacit assumption that cost of a time is independent size. This reasonable for explicit and implicit integrators use direct solvers. In context exponential integrators, however, an iterative approach, such as Krylov methods or polynomial interpolation, to compute action required matrix functions usually employed. this case, constant not valid. is, in particular, problem higher-order which are able take relatively large steps based on accuracy considerations. paper, we consider adaptive controller Rosenbrock determines premise minimizing computational cost. The largest allowed size, given by considerations, merely acts constraint. We test approach range nonlinear partial differential equations. Our results show significant improvements (up factor 4 reduction cost) over traditional wide tolerances.