Scheme of the finite element method with multiplicative separation of the singularity for a spectral boundary value problem for a degenerate differential operator
The paper deals with the numerical solution of a generalized spectral boundary value problem for an elliptic operator with degenerating coefficients. We suggest an approximate method based on the multiplicative separation of the singularity, whereby the eigenfunctions are approximated by piecewise l...
Gespeichert in:
| Veröffentlicht in: | Differential equations 2008-07, Vol.44 (7), p.999-1005 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1005 |
|---|---|
| container_issue | 7 |
| container_start_page | 999 |
| container_title | Differential equations |
| container_volume | 44 |
| creator | Lyashko, A. D. Timerbaev, M. R. |
| description | The paper deals with the numerical solution of a generalized spectral boundary value problem for an elliptic operator with degenerating coefficients. We suggest an approximate method based on the multiplicative separation of the singularity, whereby the eigenfunctions are approximated by piecewise linear functions multiplied by a weight specially chosen depending on the order of degeneration of the coefficients. For this method, we obtain error estimates justifying its optimality. |
| doi_str_mv | 10.1134/S0012266108070124 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_36416784</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1897004091</sourcerecordid><originalsourceid>FETCH-LOGICAL-c298t-972be56a4d4837612fa1722e83fe19f5c09301fdbc1d80dbb66d0363adff22463</originalsourceid><addsrcrecordid>eNp1kcFqHDEMhk1podu0D9Cb6SG3aSx71uM5lpAmhUAOac-DZyzvOnjsqe1JyevkSetlEwItOUlI3_9LSIR8BvYVQLRnt4wB51ICU6yrafuGbEAy1QimxFuyObSbQ_89-ZDzHWOs72C7IY-30x5npNHSskdqXXAFKfpaC4XOWPbR0D-u7Om8-uIW7yZd3D3SjItONY3hWZtd2K1eJ1ceqI2JapoXnErSno5xDUanB3qv_Yp0SXGsE54ogzsMWL2QGmctpjrZVVFcDsWYPpJ3VvuMn57iCfn1_eLn-VVzfXP54_zbdTPxXpWm7_iIW6lb0yrRSeBWQ8c5KmERerudWC8YWDNOYBQz4yilYUIKbazlvJXihJwefet6v1fMZZhdntB7HTCueRCyBdmptoJf_gHv4ppC3W3gYgugJOMVgiM0pZhzQjssyc31BgOw4fCy4b-XVQ0_anJlww7Ti_Hror_Ml5uM</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>235118602</pqid></control><display><type>article</type><title>Scheme of the finite element method with multiplicative separation of the singularity for a spectral boundary value problem for a degenerate differential operator</title><source>Springer Nature - Complete Springer Journals</source><creator>Lyashko, A. D. ; Timerbaev, M. R.</creator><creatorcontrib>Lyashko, A. D. ; Timerbaev, M. R.</creatorcontrib><description>The paper deals with the numerical solution of a generalized spectral boundary value problem for an elliptic operator with degenerating coefficients. We suggest an approximate method based on the multiplicative separation of the singularity, whereby the eigenfunctions are approximated by piecewise linear functions multiplied by a weight specially chosen depending on the order of degeneration of the coefficients. For this method, we obtain error estimates justifying its optimality.</description><identifier>ISSN: 0012-2661</identifier><identifier>EISSN: 1608-3083</identifier><identifier>DOI: 10.1134/S0012266108070124</identifier><language>eng</language><publisher>Dordrecht: SP MAIK Nauka/Interperiodica</publisher><subject>Approximation ; Boundary value problems ; Difference and Functional Equations ; Eigenvalues ; Estimates ; Finite element analysis ; Hilbert space ; Mathematics ; Mathematics and Statistics ; Numerical Methods ; Ordinary Differential Equations ; Partial Differential Equations ; Studies</subject><ispartof>Differential equations, 2008-07, Vol.44 (7), p.999-1005</ispartof><rights>MAIK Nauka 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c298t-972be56a4d4837612fa1722e83fe19f5c09301fdbc1d80dbb66d0363adff22463</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S0012266108070124$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S0012266108070124$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Lyashko, A. D.</creatorcontrib><creatorcontrib>Timerbaev, M. R.</creatorcontrib><title>Scheme of the finite element method with multiplicative separation of the singularity for a spectral boundary value problem for a degenerate differential operator</title><title>Differential equations</title><addtitle>Diff Equat</addtitle><description>The paper deals with the numerical solution of a generalized spectral boundary value problem for an elliptic operator with degenerating coefficients. We suggest an approximate method based on the multiplicative separation of the singularity, whereby the eigenfunctions are approximated by piecewise linear functions multiplied by a weight specially chosen depending on the order of degeneration of the coefficients. For this method, we obtain error estimates justifying its optimality.</description><subject>Approximation</subject><subject>Boundary value problems</subject><subject>Difference and Functional Equations</subject><subject>Eigenvalues</subject><subject>Estimates</subject><subject>Finite element analysis</subject><subject>Hilbert space</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Methods</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Studies</subject><issn>0012-2661</issn><issn>1608-3083</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kcFqHDEMhk1podu0D9Cb6SG3aSx71uM5lpAmhUAOac-DZyzvOnjsqe1JyevkSetlEwItOUlI3_9LSIR8BvYVQLRnt4wB51ICU6yrafuGbEAy1QimxFuyObSbQ_89-ZDzHWOs72C7IY-30x5npNHSskdqXXAFKfpaC4XOWPbR0D-u7Om8-uIW7yZd3D3SjItONY3hWZtd2K1eJ1ceqI2JapoXnErSno5xDUanB3qv_Yp0SXGsE54ogzsMWL2QGmctpjrZVVFcDsWYPpJ3VvuMn57iCfn1_eLn-VVzfXP54_zbdTPxXpWm7_iIW6lb0yrRSeBWQ8c5KmERerudWC8YWDNOYBQz4yilYUIKbazlvJXihJwefet6v1fMZZhdntB7HTCueRCyBdmptoJf_gHv4ppC3W3gYgugJOMVgiM0pZhzQjssyc31BgOw4fCy4b-XVQ0_anJlww7Ti_Hror_Ml5uM</recordid><startdate>20080701</startdate><enddate>20080701</enddate><creator>Lyashko, A. D.</creator><creator>Timerbaev, M. R.</creator><general>SP MAIK Nauka/Interperiodica</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>04Q</scope><scope>04W</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PADUT</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>PYYUZ</scope><scope>Q9U</scope></search><sort><creationdate>20080701</creationdate><title>Scheme of the finite element method with multiplicative separation of the singularity for a spectral boundary value problem for a degenerate differential operator</title><author>Lyashko, A. D. ; Timerbaev, M. R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c298t-972be56a4d4837612fa1722e83fe19f5c09301fdbc1d80dbb66d0363adff22463</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Approximation</topic><topic>Boundary value problems</topic><topic>Difference and Functional Equations</topic><topic>Eigenvalues</topic><topic>Estimates</topic><topic>Finite element analysis</topic><topic>Hilbert space</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Methods</topic><topic>Ordinary Differential Equations</topic><topic>Partial Differential Equations</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lyashko, A. D.</creatorcontrib><creatorcontrib>Timerbaev, M. R.</creatorcontrib><collection>CrossRef</collection><collection>India Database</collection><collection>India Database: Science & Technology</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Global (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering 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><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>Research Library</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Research Library China</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</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><collection>ABI/INFORM Collection China</collection><collection>ProQuest Central Basic</collection><jtitle>Differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lyashko, A. D.</au><au>Timerbaev, M. R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Scheme of the finite element method with multiplicative separation of the singularity for a spectral boundary value problem for a degenerate differential operator</atitle><jtitle>Differential equations</jtitle><stitle>Diff Equat</stitle><date>2008-07-01</date><risdate>2008</risdate><volume>44</volume><issue>7</issue><spage>999</spage><epage>1005</epage><pages>999-1005</pages><issn>0012-2661</issn><eissn>1608-3083</eissn><abstract>The paper deals with the numerical solution of a generalized spectral boundary value problem for an elliptic operator with degenerating coefficients. We suggest an approximate method based on the multiplicative separation of the singularity, whereby the eigenfunctions are approximated by piecewise linear functions multiplied by a weight specially chosen depending on the order of degeneration of the coefficients. For this method, we obtain error estimates justifying its optimality.</abstract><cop>Dordrecht</cop><pub>SP MAIK Nauka/Interperiodica</pub><doi>10.1134/S0012266108070124</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0012-2661 |
| ispartof | Differential equations, 2008-07, Vol.44 (7), p.999-1005 |
| issn | 0012-2661 1608-3083 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_36416784 |
| source | Springer Nature - Complete Springer Journals |
| subjects | Approximation Boundary value problems Difference and Functional Equations Eigenvalues Estimates Finite element analysis Hilbert space Mathematics Mathematics and Statistics Numerical Methods Ordinary Differential Equations Partial Differential Equations Studies |
| title | Scheme of the finite element method with multiplicative separation of the singularity for a spectral boundary value problem for a degenerate differential operator |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-20T16%3A27%3A41IST&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=Scheme%20of%20the%20finite%20element%20method%20with%20multiplicative%20separation%20of%20the%20singularity%20for%20a%20spectral%20boundary%20value%20problem%20for%20a%20degenerate%20differential%20operator&rft.jtitle=Differential%20equations&rft.au=Lyashko,%20A.%20D.&rft.date=2008-07-01&rft.volume=44&rft.issue=7&rft.spage=999&rft.epage=1005&rft.pages=999-1005&rft.issn=0012-2661&rft.eissn=1608-3083&rft_id=info:doi/10.1134/S0012266108070124&rft_dat=%3Cproquest_cross%3E1897004091%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=235118602&rft_id=info:pmid/&rfr_iscdi=true |