HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation
Based on the multilevel interpolation theory, we constructed a meshless adaptive multiscale interpolation operator (MAMIO) with the radial basis function. Using this operator, any nonlinear partial differential equations such as Burgers equation can be discretized adaptively in physical spaces as a...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/248246 |
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| _version_ | 1849400644318789632 |
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| author | Shu-Li Mei |
| author_facet | Shu-Li Mei |
| author_sort | Shu-Li Mei |
| collection | DOAJ |
| description | Based on the multilevel interpolation theory, we constructed a meshless adaptive multiscale interpolation operator (MAMIO) with the radial basis function. Using this operator, any nonlinear partial differential equations such as Burgers equation can be discretized adaptively in physical spaces as a nonlinear matrix ordinary differential equation. In order to obtain the analytical solution of the system of ODEs, the homotopy analysis method (HAM) proposed by Shijun Liao was developed to solve the system of ODEs by combining the precise integration method (PIM) which can be employed to get the analytical solution of linear system of ODEs. The numerical experiences show that HAM is not sensitive to the time step, and so the arithmetic error is mainly derived from the discrete in physical space. |
| format | Article |
| id | doaj-art-82c54d7bc55f4b3abca5eb700145025c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-82c54d7bc55f4b3abca5eb700145025c2025-08-20T03:37:57ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/248246248246HAM-Based Adaptive Multiscale Meshless Method for Burgers EquationShu-Li Mei0College of Information and Electrical Engineering, China Agricultural University, 17 Qinghua Donglu Road, East Campus, Haidian District, Post box 53, Beijing 100083, ChinaBased on the multilevel interpolation theory, we constructed a meshless adaptive multiscale interpolation operator (MAMIO) with the radial basis function. Using this operator, any nonlinear partial differential equations such as Burgers equation can be discretized adaptively in physical spaces as a nonlinear matrix ordinary differential equation. In order to obtain the analytical solution of the system of ODEs, the homotopy analysis method (HAM) proposed by Shijun Liao was developed to solve the system of ODEs by combining the precise integration method (PIM) which can be employed to get the analytical solution of linear system of ODEs. The numerical experiences show that HAM is not sensitive to the time step, and so the arithmetic error is mainly derived from the discrete in physical space.http://dx.doi.org/10.1155/2013/248246 |
| spellingShingle | Shu-Li Mei HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation Journal of Applied Mathematics |
| title | HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation |
| title_full | HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation |
| title_fullStr | HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation |
| title_full_unstemmed | HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation |
| title_short | HAM-Based Adaptive Multiscale Meshless Method for Burgers Equation |
| title_sort | ham based adaptive multiscale meshless method for burgers equation |
| url | http://dx.doi.org/10.1155/2013/248246 |
| work_keys_str_mv | AT shulimei hambasedadaptivemultiscalemeshlessmethodforburgersequation |