A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation
A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/438289 |
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| author | Liquan Mei Yali Gao Zhangxin Chen |
| author_facet | Liquan Mei Yali Gao Zhangxin Chen |
| author_sort | Liquan Mei |
| collection | DOAJ |
| description | A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method. |
| format | Article |
| id | doaj-art-c9c239e6f34f499b8547f3f415eba933 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-c9c239e6f34f499b8547f3f415eba9332025-02-03T01:12:45ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/438289438289A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave EquationLiquan Mei0Yali Gao1Zhangxin Chen2Center for Computational Geosciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaCenter for Computational Geosciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, ChinaDepartment of Chemical & Petroleum Engineering, Schulich School of Engineering, University of Calgary, Calgary, AB, T2N 1N4, CanadaA Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time. In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method. A Fourier stability analysis for the method is shown to be marginally stable. Three invariants of motion are investigated. Numerical experiments are presented to check the theoretical study of this method.http://dx.doi.org/10.1155/2014/438289 |
| spellingShingle | Liquan Mei Yali Gao Zhangxin Chen A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation Abstract and Applied Analysis |
| title | A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation |
| title_full | A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation |
| title_fullStr | A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation |
| title_full_unstemmed | A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation |
| title_short | A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation |
| title_sort | galerkin finite element method for numerical solutions of the modified regularized long wave equation |
| url | http://dx.doi.org/10.1155/2014/438289 |
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