Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps
An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in ℝ d ( d ≥ 1 ) . The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially...
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| Veröffentlicht in: | Numerical algorithms 2021-06, Vol.87 (2), p.895-919 |
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| creator | Omelyan, Igor Kozitsky, Yuri Pilorz, Krzysztof |
| description | An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in
ℝ
d
(
d
≥
1
)
. The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The numerical algorithm which we use to solve it is based on a space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, and adjustable system-size schemes. We show that, for special choices of the model parameters, the solutions manifest unusual time behavior. A numerical error analysis of the obtained results is also carried out. |
| doi_str_mv | 10.1007/s11075-020-00992-9 |
| format | Article |
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ℝ
d
(
d
≥
1
)
. The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The numerical algorithm which we use to solve it is based on a space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, and adjustable system-size schemes. We show that, for special choices of the model parameters, the solutions manifest unusual time behavior. A numerical error analysis of the obtained results is also carried out.</description><identifier>ISSN: 1017-1398</identifier><identifier>EISSN: 1572-9265</identifier><identifier>DOI: 10.1007/s11075-020-00992-9</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Boundary conditions ; Computer Science ; Differential equations ; Error analysis ; Kinetic equations ; Mathematical models ; Mathematics ; Mathematics, Applied ; Numeric Computing ; Numerical Analysis ; Original Paper ; Physical Sciences ; Plankton ; Runge-Kutta method ; Science & Technology ; Theory of Computation</subject><ispartof>Numerical algorithms, 2021-06, Vol.87 (2), p.895-919</ispartof><rights>The Author(s) 2020</rights><rights>The Author(s) 2020. 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><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>true</woscitedreferencessubscribed><woscitedreferencescount>1</woscitedreferencescount><woscitedreferencesoriginalsourcerecordid>wos000560988000001</woscitedreferencesoriginalsourcerecordid><citedby>FETCH-LOGICAL-c363t-9f5a3856a31b7aaec2b90e814ad85a6ff80eae7a832b3750468ffc520fe65e6a3</citedby><cites>FETCH-LOGICAL-c363t-9f5a3856a31b7aaec2b90e814ad85a6ff80eae7a832b3750468ffc520fe65e6a3</cites><orcidid>0000-0003-2596-3260</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/s11075-020-00992-9$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11075-020-00992-9$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>315,781,785,27929,27930,39263,41493,42562,51324</link.rule.ids></links><search><creatorcontrib>Omelyan, Igor</creatorcontrib><creatorcontrib>Kozitsky, Yuri</creatorcontrib><creatorcontrib>Pilorz, Krzysztof</creatorcontrib><title>Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps</title><title>Numerical algorithms</title><addtitle>Numer Algor</addtitle><addtitle>NUMER ALGORITHMS</addtitle><description>An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in
ℝ
d
(
d
≥
1
)
. The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The numerical algorithm which we use to solve it is based on a space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, and adjustable system-size schemes. We show that, for special choices of the model parameters, the solutions manifest unusual time behavior. A numerical error analysis of the obtained results is also carried out.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Boundary conditions</subject><subject>Computer Science</subject><subject>Differential equations</subject><subject>Error analysis</subject><subject>Kinetic equations</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics, Applied</subject><subject>Numeric Computing</subject><subject>Numerical Analysis</subject><subject>Original Paper</subject><subject>Physical Sciences</subject><subject>Plankton</subject><subject>Runge-Kutta method</subject><subject>Science & Technology</subject><subject>Theory of Computation</subject><issn>1017-1398</issn><issn>1572-9265</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>HGBXW</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><recordid>eNqNkE1PHSEUhifGJn7UP-CKpMtm9ACXGViam1ZNTLpp14TLPSi3MzACU-MP6P-W6xi7a2TD1_McOG_TnFO4oAD9ZaYUetECgxZAKdaqg-aYir4uWCcO6xpo31Ku5FFzkvMOoGqsP27-Xg33MfnyMBIXEwnziMlbM5Ach7n4GDIpkZQHJL99wOItwcfZ7C9IdMSQPNVNxac4zcNyvn0OZvQ2kzFucSBPtTix0QyYLQaLxIQtSVjx7P8g2c3jlD83n5wZMp69zafNr-_ffq5v2rsf17frq7vW8o6XVjlhuBSd4XTTG4OWbRSgpCuzlcJ0zklAg72RnG14L2DVSeesYOCwE1i10-bLUndK8XHGXPQuzinUJzVTVHZ0JSivFFsom2LOCZ2ekh9NetYU9D5uvcSta9z6NW6tqvR1kZ5wE122ft_ruwgAogMlJewHrbT8OL325TXZdZxDqSpf1FzxcI_pXw__-d4L31em4w</recordid><startdate>20210601</startdate><enddate>20210601</enddate><creator>Omelyan, Igor</creator><creator>Kozitsky, Yuri</creator><creator>Pilorz, Krzysztof</creator><general>Springer US</general><general>Springer Nature</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>BLEPL</scope><scope>DTL</scope><scope>HGBXW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>L6V</scope><scope>M7S</scope><scope>P62</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><orcidid>https://orcid.org/0000-0003-2596-3260</orcidid></search><sort><creationdate>20210601</creationdate><title>Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps</title><author>Omelyan, Igor ; Kozitsky, Yuri ; Pilorz, Krzysztof</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c363t-9f5a3856a31b7aaec2b90e814ad85a6ff80eae7a832b3750468ffc520fe65e6a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Boundary conditions</topic><topic>Computer Science</topic><topic>Differential equations</topic><topic>Error analysis</topic><topic>Kinetic equations</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics, Applied</topic><topic>Numeric Computing</topic><topic>Numerical Analysis</topic><topic>Original Paper</topic><topic>Physical Sciences</topic><topic>Plankton</topic><topic>Runge-Kutta method</topic><topic>Science & Technology</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Omelyan, Igor</creatorcontrib><creatorcontrib>Kozitsky, Yuri</creatorcontrib><creatorcontrib>Pilorz, Krzysztof</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>Web of Science Core Collection</collection><collection>Science Citation Index Expanded</collection><collection>Web of Science - Science Citation Index Expanded - 2021</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ProQuest Central Student</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer Science Database</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><jtitle>Numerical algorithms</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Omelyan, Igor</au><au>Kozitsky, Yuri</au><au>Pilorz, Krzysztof</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps</atitle><jtitle>Numerical algorithms</jtitle><stitle>Numer Algor</stitle><stitle>NUMER ALGORITHMS</stitle><date>2021-06-01</date><risdate>2021</risdate><volume>87</volume><issue>2</issue><spage>895</spage><epage>919</epage><pages>895-919</pages><issn>1017-1398</issn><eissn>1572-9265</eissn><abstract>An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in
ℝ
d
(
d
≥
1
)
. The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The numerical algorithm which we use to solve it is based on a space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, and adjustable system-size schemes. We show that, for special choices of the model parameters, the solutions manifest unusual time behavior. A numerical error analysis of the obtained results is also carried out.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11075-020-00992-9</doi><tpages>25</tpages><orcidid>https://orcid.org/0000-0003-2596-3260</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Algebra Algorithms Boundary conditions Computer Science Differential equations Error analysis Kinetic equations Mathematical models Mathematics Mathematics, Applied Numeric Computing Numerical Analysis Original Paper Physical Sciences Plankton Runge-Kutta method Science & Technology Theory of Computation |
| title | Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps |
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