Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients
We develop a new compact scheme for the second-order PDE (parabolic and Schrödinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference ope...
Gespeichert in:
| Veröffentlicht in: | Journal of computational physics 2018-12, Vol.375, p.1451-1468 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1468 |
|---|---|
| container_issue | |
| container_start_page | 1451 |
| container_title | Journal of computational physics |
| container_volume | 375 |
| creator | Gordin, Vladimir A. Tsymbalov, Evgenii A. |
| description | We develop a new compact scheme for the second-order PDE (parabolic and Schrödinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference operator is almost self-adjoint.
•High order compact scheme for 1D parabolic and Schrodinger-type equations with variable coefficients is constructed.•The approximation order was confirmed by various numerical experiments.•The Richardson extrapolation method improves the approximation order up to 6th.•High-order Neumann boundary conditions approximation are constructed. |
| doi_str_mv | 10.1016/j.jcp.2018.06.079 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2153612321</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><els_id>S0021999118305965</els_id><sourcerecordid>2153612321</sourcerecordid><originalsourceid>FETCH-LOGICAL-c325t-bdf815bfe5be8fa93df61cd44328fb51f0cc40b6fe3573dca660b2c10c5a49113</originalsourceid><addsrcrecordid>eNp9kE1u2zAQRomiBeqmOUB3BLqWOkNJtISuCqN_QIAs0q4JcjiMKdiiQsopcrFcIBerDHfd1Wy-983ME-IDQo2A-tNYjzTXCrCvQdewHV6JDcIAldqifi02AAqrYRjwrXhXyggAfdf2G-F26ThbWqSPIXDmiVgW2vORZUhZzjZblw6RpJ28vKN9fnn2cbrnXC1PM0t-ONklpqnIP3HZy0ebo3UHlpQ4hEiRp6W8F2-CPRS-_jevxO9vX3_tflQ3t99_7r7cVNSobqmcDz12LnDnuA92aHzQSL5tG9UH12EAohacDtx028aT1RqcIgTqbDsgNlfi46V3zunhxGUxYzrlaV1pFHaNRtWocwovKcqplMzBzDkebX4yCOas0oxmVWnOKg1os6pcmc8XhtfzHyNnU86vEfuYmRbjU_wP_RdeFn7L</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2153612321</pqid></control><display><type>article</type><title>Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients</title><source>ScienceDirect Journals (5 years ago - present)</source><creator>Gordin, Vladimir A. ; Tsymbalov, Evgenii A.</creator><creatorcontrib>Gordin, Vladimir A. ; Tsymbalov, Evgenii A.</creatorcontrib><description>We develop a new compact scheme for the second-order PDE (parabolic and Schrödinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference operator is almost self-adjoint.
•High order compact scheme for 1D parabolic and Schrodinger-type equations with variable coefficients is constructed.•The approximation order was confirmed by various numerical experiments.•The Richardson extrapolation method improves the approximation order up to 6th.•High-order Neumann boundary conditions approximation are constructed.</description><identifier>ISSN: 0021-9991</identifier><identifier>EISSN: 1090-2716</identifier><identifier>DOI: 10.1016/j.jcp.2018.06.079</identifier><language>eng</language><publisher>Cambridge: Elsevier Inc</publisher><subject>Compact difference scheme ; Computational physics ; Dirichlet problem ; Finite difference method ; Finite differences ; Implicit scheme ; Matrix ; Neumann boundary conditions ; Operators (mathematics) ; Parabolic equation ; Partial differential equations ; Self-adjointness ; Test functions</subject><ispartof>Journal of computational physics, 2018-12, Vol.375, p.1451-1468</ispartof><rights>2018 Elsevier Inc.</rights><rights>Copyright Elsevier Science Ltd. Dec 15, 2018</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c325t-bdf815bfe5be8fa93df61cd44328fb51f0cc40b6fe3573dca660b2c10c5a49113</citedby><cites>FETCH-LOGICAL-c325t-bdf815bfe5be8fa93df61cd44328fb51f0cc40b6fe3573dca660b2c10c5a49113</cites><orcidid>0000-0003-4740-4638</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jcp.2018.06.079$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,780,784,3548,27922,27923,45993</link.rule.ids></links><search><creatorcontrib>Gordin, Vladimir A.</creatorcontrib><creatorcontrib>Tsymbalov, Evgenii A.</creatorcontrib><title>Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients</title><title>Journal of computational physics</title><description>We develop a new compact scheme for the second-order PDE (parabolic and Schrödinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference operator is almost self-adjoint.
•High order compact scheme for 1D parabolic and Schrodinger-type equations with variable coefficients is constructed.•The approximation order was confirmed by various numerical experiments.•The Richardson extrapolation method improves the approximation order up to 6th.•High-order Neumann boundary conditions approximation are constructed.</description><subject>Compact difference scheme</subject><subject>Computational physics</subject><subject>Dirichlet problem</subject><subject>Finite difference method</subject><subject>Finite differences</subject><subject>Implicit scheme</subject><subject>Matrix</subject><subject>Neumann boundary conditions</subject><subject>Operators (mathematics)</subject><subject>Parabolic equation</subject><subject>Partial differential equations</subject><subject>Self-adjointness</subject><subject>Test functions</subject><issn>0021-9991</issn><issn>1090-2716</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9kE1u2zAQRomiBeqmOUB3BLqWOkNJtISuCqN_QIAs0q4JcjiMKdiiQsopcrFcIBerDHfd1Wy-983ME-IDQo2A-tNYjzTXCrCvQdewHV6JDcIAldqifi02AAqrYRjwrXhXyggAfdf2G-F26ThbWqSPIXDmiVgW2vORZUhZzjZblw6RpJ28vKN9fnn2cbrnXC1PM0t-ONklpqnIP3HZy0ebo3UHlpQ4hEiRp6W8F2-CPRS-_jevxO9vX3_tflQ3t99_7r7cVNSobqmcDz12LnDnuA92aHzQSL5tG9UH12EAohacDtx028aT1RqcIgTqbDsgNlfi46V3zunhxGUxYzrlaV1pFHaNRtWocwovKcqplMzBzDkebX4yCOas0oxmVWnOKg1os6pcmc8XhtfzHyNnU86vEfuYmRbjU_wP_RdeFn7L</recordid><startdate>20181215</startdate><enddate>20181215</enddate><creator>Gordin, Vladimir A.</creator><creator>Tsymbalov, Evgenii A.</creator><general>Elsevier Inc</general><general>Elsevier Science Ltd</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>7U5</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0003-4740-4638</orcidid></search><sort><creationdate>20181215</creationdate><title>Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients</title><author>Gordin, Vladimir A. ; Tsymbalov, Evgenii A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c325t-bdf815bfe5be8fa93df61cd44328fb51f0cc40b6fe3573dca660b2c10c5a49113</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Compact difference scheme</topic><topic>Computational physics</topic><topic>Dirichlet problem</topic><topic>Finite difference method</topic><topic>Finite differences</topic><topic>Implicit scheme</topic><topic>Matrix</topic><topic>Neumann boundary conditions</topic><topic>Operators (mathematics)</topic><topic>Parabolic equation</topic><topic>Partial differential equations</topic><topic>Self-adjointness</topic><topic>Test functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gordin, Vladimir A.</creatorcontrib><creatorcontrib>Tsymbalov, Evgenii A.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Journal of computational physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gordin, Vladimir A.</au><au>Tsymbalov, Evgenii A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients</atitle><jtitle>Journal of computational physics</jtitle><date>2018-12-15</date><risdate>2018</risdate><volume>375</volume><spage>1451</spage><epage>1468</epage><pages>1451-1468</pages><issn>0021-9991</issn><eissn>1090-2716</eissn><abstract>We develop a new compact scheme for the second-order PDE (parabolic and Schrödinger type) with a variable time-independent coefficient. It has a higher order and smaller error than classic implicit scheme. The Dirichlet and Neumann boundary problems are considered. The relative finite-difference operator is almost self-adjoint.
•High order compact scheme for 1D parabolic and Schrodinger-type equations with variable coefficients is constructed.•The approximation order was confirmed by various numerical experiments.•The Richardson extrapolation method improves the approximation order up to 6th.•High-order Neumann boundary conditions approximation are constructed.</abstract><cop>Cambridge</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jcp.2018.06.079</doi><tpages>18</tpages><orcidid>https://orcid.org/0000-0003-4740-4638</orcidid></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-9991 |
| ispartof | Journal of computational physics, 2018-12, Vol.375, p.1451-1468 |
| issn | 0021-9991 1090-2716 |
| language | eng |
| recordid | cdi_proquest_journals_2153612321 |
| source | ScienceDirect Journals (5 years ago - present) |
| subjects | Compact difference scheme Computational physics Dirichlet problem Finite difference method Finite differences Implicit scheme Matrix Neumann boundary conditions Operators (mathematics) Parabolic equation Partial differential equations Self-adjointness Test functions |
| title | Compact difference scheme for parabolic and Schrödinger-type equations with variable coefficients |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T03%3A38%3A12IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Compact%20difference%20scheme%20for%20parabolic%20and%20Schr%C3%B6dinger-type%20equations%20with%20variable%20coefficients&rft.jtitle=Journal%20of%20computational%20physics&rft.au=Gordin,%20Vladimir%20A.&rft.date=2018-12-15&rft.volume=375&rft.spage=1451&rft.epage=1468&rft.pages=1451-1468&rft.issn=0021-9991&rft.eissn=1090-2716&rft_id=info:doi/10.1016/j.jcp.2018.06.079&rft_dat=%3Cproquest_cross%3E2153612321%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=2153612321&rft_id=info:pmid/&rft_els_id=S0021999118305965&rfr_iscdi=true |