The aim of this paper is to analyze explicit exponential Runge-Kutta methods for the time integration of semilinear parabolic problems. The analysis is performed in an abstract Banach space framework ...

We apply Runge-Kutta methods to linear partial differential equations of the form u t (x, t) = L (x, ∂)u (x, t) + f (x, t). Under appropriate assumptions on the eigenvalues of the operator L and the ...