Second weak order explicit stabilized methods for stiff stochastic differential equations
We introduce a new family of explicit integrators for stiff Itˆo stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of onestep stabilized methods with extended stability domains and do not suffer from stepsize reduction that standard explicit meth...
| Autores principales: | , , |
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| Formato: | Journal article |
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2012
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| _version_ | 1826282863936405504 |
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| author | Abdulle, A Vilmart, G Zygalakis, K |
| author_facet | Abdulle, A Vilmart, G Zygalakis, K |
| author_sort | Abdulle, A |
| collection | OXFORD |
| description | We introduce a new family of explicit integrators for stiff Itˆo stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of onestep stabilized methods with extended stability domains and do not suffer from stepsize reduction that standard explicit methods face. The family is based on the classical stabilized methods of order two for deterministic problems and its construction relies on the strategy of modified equations recently introduced for SDEs. The convergence and the stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations (SPDEs), are presented and confirm the theoretical results. |
| first_indexed | 2024-03-07T00:50:16Z |
| format | Journal article |
| id | oxford-uuid:8626650a-a67d-4027-beb7-2a5ad433b7e6 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:50:16Z |
| publishDate | 2012 |
| record_format | dspace |
| spelling | oxford-uuid:8626650a-a67d-4027-beb7-2a5ad433b7e62022-03-26T22:02:04ZSecond weak order explicit stabilized methods for stiff stochastic differential equationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8626650a-a67d-4027-beb7-2a5ad433b7e6Mathematical Institute - ePrints2012Abdulle, AVilmart, GZygalakis, KWe introduce a new family of explicit integrators for stiff Itˆo stochastic differential equations (SDEs) of weak order two. These numerical methods belong to the class of onestep stabilized methods with extended stability domains and do not suffer from stepsize reduction that standard explicit methods face. The family is based on the classical stabilized methods of order two for deterministic problems and its construction relies on the strategy of modified equations recently introduced for SDEs. The convergence and the stability properties of the methods are analyzed. Numerical experiments, including applications to nonlinear SDEs and parabolic stochastic partial differential equations (SPDEs), are presented and confirm the theoretical results. |
| spellingShingle | Abdulle, A Vilmart, G Zygalakis, K Second weak order explicit stabilized methods for stiff stochastic differential equations |
| title | Second weak order explicit stabilized methods for stiff
stochastic differential equations |
| title_full | Second weak order explicit stabilized methods for stiff
stochastic differential equations |
| title_fullStr | Second weak order explicit stabilized methods for stiff
stochastic differential equations |
| title_full_unstemmed | Second weak order explicit stabilized methods for stiff
stochastic differential equations |
| title_short | Second weak order explicit stabilized methods for stiff
stochastic differential equations |
| title_sort | second weak order explicit stabilized methods for stiff stochastic differential equations |
| work_keys_str_mv | AT abdullea secondweakorderexplicitstabilizedmethodsforstiffstochasticdifferentialequations AT vilmartg secondweakorderexplicitstabilizedmethodsforstiffstochasticdifferentialequations AT zygalakisk secondweakorderexplicitstabilizedmethodsforstiffstochasticdifferentialequations |