Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems

In this paper we consider the case of nonlinear convectiondiffusion problems with a dominating convection term and we propose exponential integrators based on the composition of exact pure convection flows. The main reason for developing this type of methods is that as it turns out they can be applied to the numerical integration of the considered PDEs in a semi-Lagrangian fashion. SemiLagrangian methods perform well on convection dominated problems [Pi], [HE], [RM], [Ba]. In these methods linear convective terms are integrated exactly by first computing the characteristics corresponding to the gridponts of the adopted discretization, and then producing the numerical approximation via an interpolation procedure.