Numerical approximation of nonlinear SPDE’s
The numerical analysis of stochastic parabolic partial differential equations of the form d u + A ( u ) d t = f d t + g d W , is surveyed, where A is a nonlinear partial operator and W a Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framew...
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Veröffentlicht in: | Stochastic partial differential equations : analysis and computations 2023-12, Vol.11 (4), p.1553-1634 |
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container_title | Stochastic partial differential equations : analysis and computations |
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creator | Ondreját, Martin Prohl, Andreas Walkington, Noel J. |
description | The numerical analysis of stochastic parabolic partial differential equations of the form
d
u
+
A
(
u
)
d
t
=
f
d
t
+
g
d
W
,
is surveyed, where
A
is a nonlinear partial operator and
W
a Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory. |
doi_str_mv | 10.1007/s40072-022-00271-9 |
format | Article |
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d
u
+
A
(
u
)
d
t
=
f
d
t
+
g
d
W
,
is surveyed, where
A
is a nonlinear partial operator and
W
a Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory.</description><identifier>ISSN: 2194-0401</identifier><identifier>EISSN: 2194-041X</identifier><identifier>DOI: 10.1007/s40072-022-00271-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Approximation ; Computational Mathematics and Numerical Analysis ; Computational Science and Engineering ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Numerical Analysis ; Parabolic differential equations ; Partial Differential Equations ; Probability Theory and Stochastic Processes ; Statistical Theory and Methods</subject><ispartof>Stochastic partial differential equations : analysis and computations, 2023-12, Vol.11 (4), p.1553-1634</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c363t-bb9051546925cb44915464de922c30b2148620ca2fb692e7df8f28c9537dd9983</citedby><cites>FETCH-LOGICAL-c363t-bb9051546925cb44915464de922c30b2148620ca2fb692e7df8f28c9537dd9983</cites><orcidid>0000-0003-4523-9536</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s40072-022-00271-9$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40072-022-00271-9$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Ondreját, Martin</creatorcontrib><creatorcontrib>Prohl, Andreas</creatorcontrib><creatorcontrib>Walkington, Noel J.</creatorcontrib><title>Numerical approximation of nonlinear SPDE’s</title><title>Stochastic partial differential equations : analysis and computations</title><addtitle>Stoch PDE: Anal Comp</addtitle><description>The numerical analysis of stochastic parabolic partial differential equations of the form
d
u
+
A
(
u
)
d
t
=
f
d
t
+
g
d
W
,
is surveyed, where
A
is a nonlinear partial operator and
W
a Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory.</description><subject>Approximation</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Computational Science and Engineering</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><subject>Parabolic differential equations</subject><subject>Partial Differential Equations</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Statistical Theory and Methods</subject><issn>2194-0401</issn><issn>2194-041X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><recordid>eNp9UMFKxDAUDKLgsu4PeCp4jr68JE1zlHV1hUUFFbyFNk2ly25bkxb05m_4e36JWSt68_Dem8PMvGEIOWZwygDUWRBxIwWMA6gY1XtkgkwLCoI97f9iYIdkFsIaABhPFUM5IfRm2Dpf23yT5F3n29d6m_d12yRtlTRts6kbl_vk_u5i8fn-EY7IQZVvgpv93Cl5vFw8zJd0dXt1PT9fUctT3tOi0CCZFKlGaQsh9A6L0mlEy6FAJrIUweZYFZHiVFllFWZWS67KUuuMT8nJ6BsTvQwu9GbdDr6JLw1mCrhEKWVk4ciyvg3Bu8p0Psb3b4aB2TVjxmZMbMZ8N2N0FPFRFCK5eXb-z_of1ReEEWRi</recordid><startdate>20231201</startdate><enddate>20231201</enddate><creator>Ondreját, Martin</creator><creator>Prohl, Andreas</creator><creator>Walkington, Noel J.</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0003-4523-9536</orcidid></search><sort><creationdate>20231201</creationdate><title>Numerical approximation of nonlinear SPDE’s</title><author>Ondreját, Martin ; Prohl, Andreas ; Walkington, Noel J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-bb9051546925cb44915464de922c30b2148620ca2fb692e7df8f28c9537dd9983</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Approximation</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Computational Science and Engineering</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><topic>Parabolic differential equations</topic><topic>Partial Differential Equations</topic><topic>Probability Theory and Stochastic Processes</topic><topic>Statistical Theory and Methods</topic><toplevel>online_resources</toplevel><creatorcontrib>Ondreját, Martin</creatorcontrib><creatorcontrib>Prohl, Andreas</creatorcontrib><creatorcontrib>Walkington, Noel J.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</collection><jtitle>Stochastic partial differential equations : analysis and computations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ondreját, Martin</au><au>Prohl, Andreas</au><au>Walkington, Noel J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical approximation of nonlinear SPDE’s</atitle><jtitle>Stochastic partial differential equations : analysis and computations</jtitle><stitle>Stoch PDE: Anal Comp</stitle><date>2023-12-01</date><risdate>2023</risdate><volume>11</volume><issue>4</issue><spage>1553</spage><epage>1634</epage><pages>1553-1634</pages><issn>2194-0401</issn><eissn>2194-041X</eissn><abstract>The numerical analysis of stochastic parabolic partial differential equations of the form
d
u
+
A
(
u
)
d
t
=
f
d
t
+
g
d
W
,
is surveyed, where
A
is a nonlinear partial operator and
W
a Brownian motion. This manuscript unifies much of the theory developed over the last decade into a cohesive framework which integrates techniques for the approximation of deterministic partial differential equations with methods for the approximation of stochastic ordinary differential equations. The manuscript is intended to be accessible to audiences versed in either of these disciplines, and examples are presented to illustrate the applicability of the theory.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s40072-022-00271-9</doi><tpages>82</tpages><orcidid>https://orcid.org/0000-0003-4523-9536</orcidid><oa>free_for_read</oa></addata></record> |
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subjects | Approximation Computational Mathematics and Numerical Analysis Computational Science and Engineering Mathematical analysis Mathematics Mathematics and Statistics Numerical Analysis Parabolic differential equations Partial Differential Equations Probability Theory and Stochastic Processes Statistical Theory and Methods |
title | Numerical approximation of nonlinear SPDE’s |
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