Exponential Runge-Kutta methods for parabolic problems

@inproceedings{Hochbruck2004ExponentialRM,
  title={Exponential Runge-Kutta methods for parabolic problems},
  author={Marlis Hochbruck and Alexander Ostermann},
  year={2004}
}
The aim of this paper is to to construct exponential Runge-Kutta methods of collocation type and to analyze their convergence properties for linear and semilinear parabolic problems. For the analysis, an abstract Banach space framework of sectorial operators and locally Lipschitz continuous nonlinearities is chosen. This framework includes interesting examples like reaction-diffusion equations. It is shown that the methods converge at least with their stage order, and that convergence of higher… CONTINUE READING