A Linear Implicit Finite Difference Discretization of the Schrödinger–Hirota Equation
A new linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrödinger–Hirota equation. Optimal, second order convergence in the discrete H 1 -norm is proved, assuming that τ , h and τ 4 h are sufficiently small, where...
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| Veröffentlicht in: | Journal of scientific computing 2018-10, Vol.77 (1), p.634-656 |
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| container_title | Journal of scientific computing |
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| creator | Zouraris, Georgios E. |
| description | A new linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrödinger–Hirota equation. Optimal, second order convergence in the discrete
H
1
-norm is proved, assuming that
τ
,
h
and
τ
4
h
are sufficiently small, where
τ
is the time-step and
h
is the space mesh-size. The convergence analysis is based on the investigation of a modified version of the proposed finite difference method, which is innovative and handles the stability difficulties due to the presence of a nonlinear derivative term in the equation. The efficiency of the proposed finite difference method is verified by results from numerical experiments. |
| doi_str_mv | 10.1007/s10915-018-0718-6 |
| format | Article |
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H
1
-norm is proved, assuming that
τ
,
h
and
τ
4
h
are sufficiently small, where
τ
is the time-step and
h
is the space mesh-size. The convergence analysis is based on the investigation of a modified version of the proposed finite difference method, which is innovative and handles the stability difficulties due to the presence of a nonlinear derivative term in the equation. The efficiency of the proposed finite difference method is verified by results from numerical experiments.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-018-0718-6</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Approximation ; Boundary value problems ; Computational Mathematics and Numerical Analysis ; Convergence ; Error analysis ; Finite difference method ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Methods ; Numerical analysis ; Theoretical</subject><ispartof>Journal of scientific computing, 2018-10, Vol.77 (1), p.634-656</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018</rights><rights>Springer Science+Business Media, LLC, part of Springer Nature 2018.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-4afc033dd5bb7a356ae31be2743dcb1e3a361dd4b8e7ae36692f6b7c667061403</citedby><cites>FETCH-LOGICAL-c316t-4afc033dd5bb7a356ae31be2743dcb1e3a361dd4b8e7ae36692f6b7c667061403</cites><orcidid>0000-0003-0234-0175</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/s10915-018-0718-6$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2918315149?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,776,780,21368,27903,27904,33723,41467,42536,43784,51297,64361,64365,72215</link.rule.ids></links><search><creatorcontrib>Zouraris, Georgios E.</creatorcontrib><title>A Linear Implicit Finite Difference Discretization of the Schrödinger–Hirota Equation</title><title>Journal of scientific computing</title><addtitle>J Sci Comput</addtitle><description>A new linear implicit finite difference method is proposed for the approximation of the solution to a periodic, initial value problem for a Schrödinger–Hirota equation. Optimal, second order convergence in the discrete
H
1
-norm is proved, assuming that
τ
,
h
and
τ
4
h
are sufficiently small, where
τ
is the time-step and
h
is the space mesh-size. The convergence analysis is based on the investigation of a modified version of the proposed finite difference method, which is innovative and handles the stability difficulties due to the presence of a nonlinear derivative term in the equation. The efficiency of the proposed finite difference method is verified by results from numerical experiments.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Approximation</subject><subject>Boundary value problems</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Convergence</subject><subject>Error analysis</subject><subject>Finite difference method</subject><subject>Mathematical analysis</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Methods</subject><subject>Numerical 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E.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology 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>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One 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Optimal, second order convergence in the discrete
H
1
-norm is proved, assuming that
τ
,
h
and
τ
4
h
are sufficiently small, where
τ
is the time-step and
h
is the space mesh-size. The convergence analysis is based on the investigation of a modified version of the proposed finite difference method, which is innovative and handles the stability difficulties due to the presence of a nonlinear derivative term in the equation. The efficiency of the proposed finite difference method is verified by results from numerical experiments.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10915-018-0718-6</doi><tpages>23</tpages><orcidid>https://orcid.org/0000-0003-0234-0175</orcidid></addata></record> |
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| ispartof | Journal of scientific computing, 2018-10, Vol.77 (1), p.634-656 |
| issn | 0885-7474 1573-7691 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals; ProQuest Central UK/Ireland; ProQuest Central |
| subjects | Algebra Algorithms Approximation Boundary value problems Computational Mathematics and Numerical Analysis Convergence Error analysis Finite difference method Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Numerical analysis Theoretical |
| title | A Linear Implicit Finite Difference Discretization of the Schrödinger–Hirota Equation |
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