Stability under Galerkin truncation of A-stable Runge–Kutta discretizations in time
Stability under Galerkin truncation of A-stable Runge–Kutta discretizations in time
We consider semilinear evolution equations for which the linear part is normal and generates a strongly continuous semigroup, and the nonlinear part is sufficiently smooth on a scale of Hilbert spaces. We approximate their semi-flow by an implicit A-stable Runge–Kutta discretization in time and a spectral Galerkin truncation in space. …