Avoiding order reduction with explicit Runge-Kutta exponential methods in nonlinear initial boundary value problems

Abstract

In this paper a technique is given to recover the classical order of the method when explicit exponential Runge-Kutta methods integrate reaction-diffusion problems. Although methods of high stiff order for problems with vanishing boundary conditions can be constructed, that may imply increasing the number of stages and therefore, the computational cost seems bigger than the technique which is suggested here, which just adds some terms with information on the boundaries. Moreover, time-dependent boundary conditions are directly tackled here.