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KdV Equation and Computations of Solitons: Nonlinear Error Dynamics
Here we have developed new compact and hybrid schemes for the solution of KdV equation. These schemes for the third derivative have been analyzed in the spectral plane for their resolution and compared with another scheme in the literature. Furthermore the developed schemes have been used to solve a...
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| Published in: | Journal of scientific computing 2015-03, Vol.62 (3), p.693-717 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c382t-32f8fe1311130c8e3e070a89e721d911082602ad3fe8086d12b3824e7ec66b8a3 |
| container_end_page | 717 |
| container_issue | 3 |
| container_start_page | 693 |
| container_title | Journal of scientific computing |
| container_volume | 62 |
| creator | Ashwin, V. M. Saurabh, K. Sriramkrishnan, M. Bagade, P. M. Parvathi, M. K. Sengupta, Tapan K. |
| description | Here we have developed new compact and hybrid schemes for the solution of KdV equation. These schemes for the third derivative have been analyzed in the spectral plane for their resolution and compared with another scheme in the literature. Furthermore the developed schemes have been used to solve a model linear dispersion equation. The error dynamics equation has been developed for this model equation. Despite the linearity of the model equation, one can draw conclusions for error dynamics of nonlinear differential equations. The developed compact scheme has been found to be quite accurate in solving KdV equation. One- and two-soliton cases have been reported to demonstrate the above. |
| doi_str_mv | 10.1007/s10915-014-9875-4 |
| format | article |
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M. ; Saurabh, K. ; Sriramkrishnan, M. ; Bagade, P. M. ; Parvathi, M. K. ; Sengupta, Tapan K.</creator><creatorcontrib>Ashwin, V. M. ; Saurabh, K. ; Sriramkrishnan, M. ; Bagade, P. M. ; Parvathi, M. K. ; Sengupta, Tapan K.</creatorcontrib><description>Here we have developed new compact and hybrid schemes for the solution of KdV equation. These schemes for the third derivative have been analyzed in the spectral plane for their resolution and compared with another scheme in the literature. Furthermore the developed schemes have been used to solve a model linear dispersion equation. The error dynamics equation has been developed for this model equation. Despite the linearity of the model equation, one can draw conclusions for error dynamics of nonlinear differential equations. The developed compact scheme has been found to be quite accurate in solving KdV equation. One- and two-soliton cases have been reported to demonstrate the above.</description><identifier>ISSN: 0885-7474</identifier><identifier>EISSN: 1573-7691</identifier><identifier>DOI: 10.1007/s10915-014-9875-4</identifier><language>eng</language><publisher>Boston: Springer US</publisher><subject>Algorithms ; Computation ; Computational Mathematics and Numerical Analysis ; Derivatives ; Differential equations ; Errors ; Fourier transforms ; Linearity ; Mathematical analysis ; Mathematical and Computational Engineering ; Mathematical and Computational Physics ; Mathematical models ; Mathematics ; Mathematics and Statistics ; Methods ; Nonlinear differential equations ; Nonlinear dynamics ; Nonlinear equations ; Nonlinearity ; Numerical analysis ; Simulation ; Solitary waves ; Spectra ; Theoretical</subject><ispartof>Journal of scientific computing, 2015-03, Vol.62 (3), p.693-717</ispartof><rights>Springer Science+Business Media New York 2014</rights><rights>Springer Science+Business Media New York 2014.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-32f8fe1311130c8e3e070a89e721d911082602ad3fe8086d12b3824e7ec66b8a3</citedby><cites>FETCH-LOGICAL-c382t-32f8fe1311130c8e3e070a89e721d911082602ad3fe8086d12b3824e7ec66b8a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27923,27924</link.rule.ids></links><search><creatorcontrib>Ashwin, V. 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| ispartof | Journal of scientific computing, 2015-03, Vol.62 (3), p.693-717 |
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| language | eng |
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| source | Springer Nature |
| subjects | Algorithms Computation Computational Mathematics and Numerical Analysis Derivatives Differential equations Errors Fourier transforms Linearity Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematical models Mathematics Mathematics and Statistics Methods Nonlinear differential equations Nonlinear dynamics Nonlinear equations Nonlinearity Numerical analysis Simulation Solitary waves Spectra Theoretical |
| title | KdV Equation and Computations of Solitons: Nonlinear Error Dynamics |
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