|
Title
|
|
|
|
Convergence of the Hundsdorfer-Verwer scheme for two-dimensional convection-diffusion equations with mixed derivative term
|
|
|
Author
|
|
|
|
|
|
|
Abstract
|
|
|
|
| Alternating Direction Implicit (ADI) schemes are popular in the numerical solution of multidimensional time-dependent partial differential equations (PDEs) arising in various contemporary application fields such as financial mathematics. The Hundsdorfer-Verwer (HV) scheme is an often used ADI scheme. A structural analysis of its fundamental properties, notably convergence, is of main interest. Up to now, however, a convergence result is only known in the literature relevant to the case of one-dimensional PDEs. In this paper we prove that, under natural stability and smoothness conditions, the HV scheme has a temporal order of convergence equal to two, uniformly in the spatial mesh width, whenever it is applied to two-dimensional convection-diffusion equations with mixed derivative term. |
|
|
|
Language
|
|
|
|
English
|
|
|
Source (journal)
|
|
|
|
AIP conference proceedings / American Institute of Physics. - New York
|
|
|
|
|
|
|
APPLIED MATHEMATICS 2014 (ICNAAM-2014)
|
|
|
Source (book)
|
|
|
|
International Conference on Numerical Analysis and Applied Mathematics, (ICNAAM), SEP 22-28, 2014, Rhodes, GREECE
|
|
|
Publication
|
|
|
|
Melville
:
Amer inst physics
,
2015
|
|
|
ISBN
|
|
|
|
978-0-7354-1287-3
|
|
|
DOI
|
|
|
|
10.1063/1.4913109
|
|
|
Volume/pages
|
|
|
|
1648
(2015)
, 5 p.
|
|
|
ISI
|
|
|
|
000355339705106
|
|
|
Full text (Publisher's DOI)
|
|
|
|
|
|
|
Full text (open access)
|
|
|
|
|
|