An Accurate Polynomial Approximation of Exponential Integrators

摘要

Numerical time propagation of semi-linear equations such as reaction-diffusion, non-linear Schrodinger or semi-linear wave equations can be performed by the use of exponential time differencing. However, the evaluation of exponential integrators poses a serious technical complexity, particularly in multiple dimensions. In this paper we approach this difficulty by deriving simple polynomial series approximations of exponential integrators. Several numerical examples are presented.