Two linearized second-order block-centered finite difference methods for nonlinear Sobolev equations
In this paper, two efficient, linearized (or semi-implicit) Crank-Nicolson block-centered finite difference algorithms for the strongly nonlinear Sobolev equations are investigated and analyzed. Newton linearization and linear extrapolation techniques are considered to treat the nonlinear terms. It...
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| Veröffentlicht in: | Computational & applied mathematics 2023-07, Vol.42 (5), Article 222 |
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| creator | Wang, Xiaoying Fu, Hongfei |
| description | In this paper, two efficient, linearized (or semi-implicit) Crank-Nicolson block-centered finite difference algorithms for the strongly nonlinear Sobolev equations are investigated and analyzed. Newton linearization and linear extrapolation techniques are considered to treat the nonlinear terms. It is shown that on general nonuniform rectangular grids, under local Lipschitz continuous assumptions on the nonlinear coefficients and reaction terms, second-order temporal and spatial convergence are achieved for the primal scalar variable
p
, its gradient
u
and its flux
q
simultaneously. Stability of the presented algorithms are then rigorously proved under a rough time-step condition
τ
=
o
(
h
1
/
2
)
, where
τ
and
h
are, respectively, the temporal and spatial mesh sizes. Numerical experiments are presented to show the efficiency and convergence of the proposed methods. |
| doi_str_mv | 10.1007/s40314-023-02339-1 |
| format | Article |
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p
, its gradient
u
and its flux
q
simultaneously. Stability of the presented algorithms are then rigorously proved under a rough time-step condition
τ
=
o
(
h
1
/
2
)
, where
τ
and
h
are, respectively, the temporal and spatial mesh sizes. Numerical experiments are presented to show the efficiency and convergence of the proposed methods.</description><identifier>ISSN: 2238-3603</identifier><identifier>EISSN: 1807-0302</identifier><identifier>DOI: 10.1007/s40314-023-02339-1</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Algorithms ; Applications of Mathematics ; Applied physics ; Computational mathematics ; Computational Mathematics and Numerical Analysis ; Convergence ; Finite difference method ; Linearization ; Mathematical Applications in Computer Science ; Mathematical Applications in the Physical Sciences ; Mathematics ; Mathematics and Statistics</subject><ispartof>Computational & applied mathematics, 2023-07, Vol.42 (5), Article 222</ispartof><rights>The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c314t-c19dfcb7b6193285d79883d0019200fa2e60040086426b063b3bb8af4195f8083</cites><orcidid>0000-0002-8294-8086</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/s40314-023-02339-1$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s40314-023-02339-1$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Wang, Xiaoying</creatorcontrib><creatorcontrib>Fu, Hongfei</creatorcontrib><title>Two linearized second-order block-centered finite difference methods for nonlinear Sobolev equations</title><title>Computational & applied mathematics</title><addtitle>Comp. Appl. Math</addtitle><description>In this paper, two efficient, linearized (or semi-implicit) Crank-Nicolson block-centered finite difference algorithms for the strongly nonlinear Sobolev equations are investigated and analyzed. Newton linearization and linear extrapolation techniques are considered to treat the nonlinear terms. It is shown that on general nonuniform rectangular grids, under local Lipschitz continuous assumptions on the nonlinear coefficients and reaction terms, second-order temporal and spatial convergence are achieved for the primal scalar variable
p
, its gradient
u
and its flux
q
simultaneously. Stability of the presented algorithms are then rigorously proved under a rough time-step condition
τ
=
o
(
h
1
/
2
)
, where
τ
and
h
are, respectively, the temporal and spatial mesh sizes. Numerical experiments are presented to show the efficiency and convergence of the proposed methods.</description><subject>Algorithms</subject><subject>Applications of Mathematics</subject><subject>Applied physics</subject><subject>Computational mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Convergence</subject><subject>Finite difference method</subject><subject>Linearization</subject><subject>Mathematical Applications in Computer Science</subject><subject>Mathematical Applications in the Physical Sciences</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><issn>2238-3603</issn><issn>1807-0302</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEQxYMoWKtfwFPAc3SSbHezRyn-g4IH6zlskolu3SZtslX007t1BW8ehmGY994MP0LOOVxygOoqFyB5wUDIfcma8QMy4QoqBhLEIZkIIRWTJchjcpLzCkBWvCgmxC0_Iu3agE1qv9DRjDYGx2JymKjpon1jFkOPadj5NrQ9Utd6P8zBIl1j_xpdpj4mGmIYc-hTNLHDd4rbXdO3MeRTcuSbLuPZb5-S59ub5fyeLR7vHubXC2aH53tmee28NZUpeS2FmrmqVko6AF4LAN8ILAEKAFUWojRQSiONUY0veD3zCpSckosxd5Pidoe516u4S2E4qYUSVcWlKvcqMapsijkn9HqT2nWTPjUHvaepR5p6IKl_aGo-mORoyoM4vGD6i_7H9Q3dX3fY</recordid><startdate>20230701</startdate><enddate>20230701</enddate><creator>Wang, Xiaoying</creator><creator>Fu, Hongfei</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-8294-8086</orcidid></search><sort><creationdate>20230701</creationdate><title>Two linearized second-order block-centered finite difference methods for nonlinear Sobolev equations</title><author>Wang, Xiaoying ; Fu, Hongfei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c314t-c19dfcb7b6193285d79883d0019200fa2e60040086426b063b3bb8af4195f8083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algorithms</topic><topic>Applications of Mathematics</topic><topic>Applied physics</topic><topic>Computational mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Convergence</topic><topic>Finite difference method</topic><topic>Linearization</topic><topic>Mathematical Applications in Computer Science</topic><topic>Mathematical Applications in the Physical Sciences</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Xiaoying</creatorcontrib><creatorcontrib>Fu, Hongfei</creatorcontrib><collection>CrossRef</collection><jtitle>Computational & applied mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Xiaoying</au><au>Fu, Hongfei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two linearized second-order block-centered finite difference methods for nonlinear Sobolev equations</atitle><jtitle>Computational & applied mathematics</jtitle><stitle>Comp. Appl. Math</stitle><date>2023-07-01</date><risdate>2023</risdate><volume>42</volume><issue>5</issue><artnum>222</artnum><issn>2238-3603</issn><eissn>1807-0302</eissn><abstract>In this paper, two efficient, linearized (or semi-implicit) Crank-Nicolson block-centered finite difference algorithms for the strongly nonlinear Sobolev equations are investigated and analyzed. Newton linearization and linear extrapolation techniques are considered to treat the nonlinear terms. It is shown that on general nonuniform rectangular grids, under local Lipschitz continuous assumptions on the nonlinear coefficients and reaction terms, second-order temporal and spatial convergence are achieved for the primal scalar variable
p
, its gradient
u
and its flux
q
simultaneously. Stability of the presented algorithms are then rigorously proved under a rough time-step condition
τ
=
o
(
h
1
/
2
)
, where
τ
and
h
are, respectively, the temporal and spatial mesh sizes. Numerical experiments are presented to show the efficiency and convergence of the proposed methods.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40314-023-02339-1</doi><orcidid>https://orcid.org/0000-0002-8294-8086</orcidid><oa>free_for_read</oa></addata></record> |
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| subjects | Algorithms Applications of Mathematics Applied physics Computational mathematics Computational Mathematics and Numerical Analysis Convergence Finite difference method Linearization Mathematical Applications in Computer Science Mathematical Applications in the Physical Sciences Mathematics Mathematics and Statistics |
| title | Two linearized second-order block-centered finite difference methods for nonlinear Sobolev equations |
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