Numerical simulation for certain stochastic ordinary differential equations
A Monte Carlo simulation approach is presented for solving two problems based on stochastic ordinary differential equations, namely an initial-value problem for a nonlinear ordinary differential equation and a two-point boundary-value problem for a linear equation. The method consists of simulating...
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| Veröffentlicht in: | J. Comput. Phys.; (United States) 1988, Vol.74 (1), p.244-262 |
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| container_title | J. Comput. Phys.; (United States) |
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| creator | Spigler, Renato |
| description | A Monte Carlo simulation approach is presented for solving two problems based on stochastic ordinary differential equations, namely an
initial-value problem for a nonlinear ordinary differential equation
and a two-point
boundary-value problem for a linear equation. The method consists of simulating on the computer several realizations of the random process which appears in the coefficients of the equations, and then computing the average over the corresponding solutions. Since these two problems are related to the same physical problem, we are able to compare the results. Several plots are given to illustrate the results and a discussion of the various kinds of errors which affect the method is presented. |
| doi_str_mv | 10.1016/0021-9991(88)90079-4 |
| format | Article |
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initial-value problem for a nonlinear ordinary differential equation
and a two-point
boundary-value problem for a linear equation. The method consists of simulating on the computer several realizations of the random process which appears in the coefficients of the equations, and then computing the average over the corresponding solutions. Since these two problems are related to the same physical problem, we are able to compare the results. Several plots are given to illustrate the results and a discussion of the various kinds of errors which affect the method is presented.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/0021-9991(88)90079-4</identifier><language>eng</language><publisher>United States: Elsevier Inc</publisher><subject>990230 - Mathematics & Mathematical Models- (1987-1989) ; BOUNDARY-VALUE PROBLEMS ; DIFFERENTIAL EQUATIONS ; EQUATIONS ; GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE ; MONTE CARLO METHOD ; NUMERICAL SOLUTION ; WAVE PROPAGATION</subject><ispartof>J. Comput. Phys.; (United States), 1988, Vol.74 (1), p.244-262</ispartof><rights>1988</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c364t-baea84471e8c33504da9e39f109e05ca7dac7f9dc4d15a6d0c3e9494fc7308323</citedby><cites>FETCH-LOGICAL-c364t-baea84471e8c33504da9e39f109e05ca7dac7f9dc4d15a6d0c3e9494fc7308323</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/0021-9991(88)90079-4$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,885,3550,4024,27923,27924,27925,45995</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/5470079$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Spigler, Renato</creatorcontrib><creatorcontrib>Courant Institute of Mathematical Sciences, New York University, New York, New York 10012</creatorcontrib><title>Numerical simulation for certain stochastic ordinary differential equations</title><title>J. Comput. Phys.; (United States)</title><description>A Monte Carlo simulation approach is presented for solving two problems based on stochastic ordinary differential equations, namely an
initial-value problem for a nonlinear ordinary differential equation
and a two-point
boundary-value problem for a linear equation. The method consists of simulating on the computer several realizations of the random process which appears in the coefficients of the equations, and then computing the average over the corresponding solutions. Since these two problems are related to the same physical problem, we are able to compare the results. Several plots are given to illustrate the results and a discussion of the various kinds of errors which affect the method is presented.</description><subject>990230 - Mathematics & Mathematical Models- (1987-1989)</subject><subject>BOUNDARY-VALUE PROBLEMS</subject><subject>DIFFERENTIAL EQUATIONS</subject><subject>EQUATIONS</subject><subject>GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE</subject><subject>MONTE CARLO METHOD</subject><subject>NUMERICAL SOLUTION</subject><subject>WAVE PROPAGATION</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1988</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAURYMoOI7-AxfFheiimjTpNNkIMviFg250HeLLKxNpm5kkFfz3tlNx6eptzr3cdwg5ZfSKUba4prRguVKKXUh5qSitVC72yIxRRfOiYot9MvtDDslRjJ-UUlkKOSPPL32LwYFpsujavjHJ-S6rfcgAQzKuy2LysDYxOch8sK4z4Tuzrq4xYJfckMNtv0vFY3JQmybiye-dk_f7u7flY756fXha3q5y4AuR8g-DRgpRMZTAeUmFNQq5qoe5SEswlTVQ1cqCsKw0C0uBoxJK1FBxKnnB5-Rs6vXDKh3BJYQ1-K5DSLoU1ShggM4naBP8tseYdOsiYNOYDn0fdSEU42VRDaCYQAg-xoC13gTXDl9qRvWoV4_u9OhOS6l3erUYYjdTDIdPvxyGcQh2gNaFcYf17v-CH1sSgn4</recordid><startdate>1988</startdate><enddate>1988</enddate><creator>Spigler, Renato</creator><general>Elsevier Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>1988</creationdate><title>Numerical simulation for certain stochastic ordinary differential equations</title><author>Spigler, Renato</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c364t-baea84471e8c33504da9e39f109e05ca7dac7f9dc4d15a6d0c3e9494fc7308323</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1988</creationdate><topic>990230 - Mathematics & Mathematical Models- (1987-1989)</topic><topic>BOUNDARY-VALUE PROBLEMS</topic><topic>DIFFERENTIAL EQUATIONS</topic><topic>EQUATIONS</topic><topic>GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE</topic><topic>MONTE CARLO METHOD</topic><topic>NUMERICAL SOLUTION</topic><topic>WAVE PROPAGATION</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Spigler, Renato</creatorcontrib><creatorcontrib>Courant Institute of Mathematical Sciences, New York University, New York, New York 10012</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>J. Comput. Phys.; (United States)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Spigler, Renato</au><aucorp>Courant Institute of Mathematical Sciences, New York University, New York, New York 10012</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Numerical simulation for certain stochastic ordinary differential equations</atitle><jtitle>J. Comput. Phys.; (United States)</jtitle><date>1988</date><risdate>1988</risdate><volume>74</volume><issue>1</issue><spage>244</spage><epage>262</epage><pages>244-262</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>A Monte Carlo simulation approach is presented for solving two problems based on stochastic ordinary differential equations, namely an
initial-value problem for a nonlinear ordinary differential equation
and a two-point
boundary-value problem for a linear equation. The method consists of simulating on the computer several realizations of the random process which appears in the coefficients of the equations, and then computing the average over the corresponding solutions. Since these two problems are related to the same physical problem, we are able to compare the results. Several plots are given to illustrate the results and a discussion of the various kinds of errors which affect the method is presented.</abstract><cop>United States</cop><pub>Elsevier Inc</pub><doi>10.1016/0021-9991(88)90079-4</doi><tpages>19</tpages></addata></record> |
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| ispartof | J. Comput. Phys.; (United States), 1988, Vol.74 (1), p.244-262 |
| issn | 0021-9991 1090-2716 |
| language | eng |
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| source | Access via ScienceDirect (Elsevier) |
| subjects | 990230 - Mathematics & Mathematical Models- (1987-1989) BOUNDARY-VALUE PROBLEMS DIFFERENTIAL EQUATIONS EQUATIONS GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE MONTE CARLO METHOD NUMERICAL SOLUTION WAVE PROPAGATION |
| title | Numerical simulation for certain stochastic ordinary differential equations |
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