A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves
The Boussinesq equation has some application in fluid dynamics, water sciences and so forth. In the current paper, we study an improved Boussinesq model. First, a finite difference approximation is employed to discrete the derivative of the temporal variable. Then, we study the existence and uniquen...
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| Veröffentlicht in: | Numerical methods for partial differential equations 2024-05, Vol.40 (3), p.n/a |
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| container_title | Numerical methods for partial differential equations |
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| creator | Abbaszadeh, Mostafa Bagheri Salec, AliReza Hatim Aal‐Ezirej, Taghreed Abdul‐Kareem |
| description | The Boussinesq equation has some application in fluid dynamics, water sciences and so forth. In the current paper, we study an improved Boussinesq model. First, a finite difference approximation is employed to discrete the derivative of the temporal variable. Then, we study the existence and uniqueness of solution of the semi‐discrete scheme according to the fixed point theorem. In addition, the unconditional stability and convergence of the semi‐discrete scheme are presented. Then, we construct the fully discrete formulation based upon the radial basis function‐finite difference method. The convergence rate and stability of the fully‐discrete scheme are analyzed. In the end, some examples in 1D and 2D cases are studied to corroborate the capability of the proposed scheme. |
| doi_str_mv | 10.1002/num.23077 |
| format | Article |
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In the current paper, we study an improved Boussinesq model. First, a finite difference approximation is employed to discrete the derivative of the temporal variable. Then, we study the existence and uniqueness of solution of the semi‐discrete scheme according to the fixed point theorem. In addition, the unconditional stability and convergence of the semi‐discrete scheme are presented. Then, we construct the fully discrete formulation based upon the radial basis function‐finite difference method. The convergence rate and stability of the fully‐discrete scheme are analyzed. In the end, some examples in 1D and 2D cases are studied to corroborate the capability of the proposed scheme.</description><identifier>ISSN: 0749-159X</identifier><identifier>EISSN: 1098-2426</identifier><identifier>DOI: 10.1002/num.23077</identifier><language>eng</language><publisher>Hoboken, USA: John Wiley & Sons, Inc</publisher><subject>Boussinesq equations ; Convergence ; convergence and error analysis ; Finite difference method ; Fixed points (mathematics) ; Fluid dynamics ; improved Boussinesq model (IBM) ; Mathematical analysis ; Radial basis function ; radial basis functions (RBFs) ; RBFs‐finite difference (RBFs‐FD) approach ; Solitary waves ; Stability analysis</subject><ispartof>Numerical methods for partial differential equations, 2024-05, Vol.40 (3), p.n/a</ispartof><rights>2023 Wiley Periodicals LLC.</rights><rights>2024 Wiley Periodicals LLC.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c2577-5c247bcfea48b501b9cc0d8b82b956e3996553851700f6b1d83433cb750aa7ba3</cites><orcidid>0000-0001-6954-3896</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnum.23077$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnum.23077$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1417,27924,27925,45574,45575</link.rule.ids></links><search><creatorcontrib>Abbaszadeh, Mostafa</creatorcontrib><creatorcontrib>Bagheri Salec, AliReza</creatorcontrib><creatorcontrib>Hatim Aal‐Ezirej, Taghreed Abdul‐Kareem</creatorcontrib><title>A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves</title><title>Numerical methods for partial differential equations</title><description>The Boussinesq equation has some application in fluid dynamics, water sciences and so forth. 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| source | Wiley Online Library All Journals |
| subjects | Boussinesq equations Convergence convergence and error analysis Finite difference method Fixed points (mathematics) Fluid dynamics improved Boussinesq model (IBM) Mathematical analysis Radial basis function radial basis functions (RBFs) RBFs‐finite difference (RBFs‐FD) approach Solitary waves Stability analysis |
| title | A radial basis function (RBF)‐finite difference method for solving improved Boussinesq model with error estimation and description of solitary waves |
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