RT info:eu-repo/semantics/article
T1 Power boundedness in the maximum norm of stability matrices for ADI methods
A1 Hernández Abreu, Domingo
A1 González Pinto, Severiano
A1 Hairer, Ernst
A2 Análisis Matemático
A2 Grupo de investigación ULL:
"Métodos numéricos en ecuaciones diferenciales"
https://www.ull.es/grupoinvestigacion/met-numericos-ec-diferenciales/
K1 Parabolic PDEs
K1 time integration
K1 Alternating Direction Implicit schemes
K1 stability
K1 power boundedness
K1 maximum norm
AB The study of convergence of time integrators, applied to linear discretized PDEs, relies on the power boundedness of the stability matrix R. The present work investigates power boundedness in the maximum norm for ADI-type integrators in arbitrary space dimension m. Examples are the Douglas scheme, the Craig–Sneyd scheme, and W-methods with a low stage number. It is shown that for some important integrators ‖ Rn‖ ∞ is bounded in the maximum norm by a constant times min ((ln (1 + n)) m, (ln N) m) , where m is the space dimension of the PDE, and N≥ 2 is the space discretization parameter. For m≤ 2 sharper bounds are obtained that are independent of n and N.
YR 2021
FD 2021
LK http://riull.ull.es/xmlui/handle/915/39004
UL http://riull.ull.es/xmlui/handle/915/39004
LA en
DS Repositorio institucional de la Universidad de La Laguna
RD 25-nov-2024