RT info:eu-repo/semantics/article
T1 Convergence in the maximum norm of ADI-type methods for parabolic problems
A1 Hernández Abreu, Domingo
A1 Gonz´alez-Pinto, S.
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 Stability
K1 Power boundedness
K1 Convergence
K1 Maximum norm
K1 Approximate Matrix Factorization
K1 W-methods
K1 Alternating Direction Implicit schemes
AB Results on unconditional convergence in the maximum norm for ADI-type methods, such as the Douglas method, applied to the time integration of parabolic problems are quite difficult to get, mainly when the number of space dimensions m is greater than two. Such a result is obtained here under quite general conditions on a linear PDE problem in case that time-independent Dirichlet boundary conditions are imposed. To get these bounds, a theorem that guarantees, in some sense, power-boundeness of the stability function independently of both the space and time resolutions is proved.
SN 0168-9274
YR 2022
FD 2022
LK http://riull.ull.es/xmlui/handle/915/39010
UL http://riull.ull.es/xmlui/handle/915/39010
LA en
DS Repositorio institucional de la Universidad de La Laguna
RD 18-dic-2024