Convergence in l_2 and l_∞ norm of one-stage AMF-W-methods for parabolic problems
Severiano González-Pinto, Ernst Hairer, and Domingo Hernández-Abreu,
Abstract. For the numerical solution of parabolic problems with linear diffusion term,
linearly implicit time integrators are considered. To reduce the cost on the linear algebra level
an alternating direction implicit (ADI) approach is applied (so-called AMF-W-methods).
The present work proves optimal bounds of the global error
for two classes of 1-stage methods in the Euclidean l_2 norm as well as
in the maximum norm l_∞.
The bounds are valid under a very weak step size restriction that covers PDE-convergence,
where the time step size is of the same order as the spatial grid size.
Key Words. Parabolic PDEs, time integration, W-methods,
Approximate Matrix Factorization, Alternating Direction Implicit schemes, convergence.