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| ADAPTIVE INTERVAL WAVELET PRECISE INTEGRATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS | |
| 作者姓名： | 梅树立 陆启韶 张森文 金俐 |
| 作者单位： | College of Information and Electrical Engineering，China Agricultural University，Beijing 100083，P.R. China，School of Sciences，Beijing University of Aeronautics and Astronautics，Beijing 100083，P.R. China，The Institute of Applied Mechanics，Jinan University，Guangzhou 510632，P.R. China，College of Information and Electrical Engineering，China Agricultural University，Beijing 100083，P.R. China |
| 基金项目： | ProjectsupportedbytheNationalNaturalScienceFoundationofChina (Nos.1 0 3 72 0 3 6，1 0 1 72 0 1 1 ) |
| 摘 要： | IntroductionThepreciseintegrationmethod(PIM) 1],whichwasproposedforsolvingstructuraldynamicequations.Thismethodissimplerandpossesseshigherprecision .Forlinearsteadystructuraldynamicsystems,itsnumericalresultsattheintegrationpointsarealmostequaltothatoftheexactsolutioninmachineaccuracy .InthepreciseintegrationmethodforsolvingPDEs,theequationsshouldbediscretizedinthephysicalspaceforobtainingthesystemofODEsintime ,whichisoftenexecutedbythefinitedifferencemethodorthefiniteelementmethod .Inrec… |
| 关 键 词： | 综合精确法 外推法 伯格斯函数 时间间隔 小波变换 流体动力学 |
| 收稿时间： | 30 June 2003 |
Adaptive interval wavelet precise integration method for partial differential equations |
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| Mei Shu-li Doctor,Lu Qi-shao Professor,Zhang Sen-wen,Jin Li.ADAPTIVE INTERVAL WAVELET PRECISE INTEGRATION METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS[J].Applied Mathematics and Mechanics(English Edition),2005,26(3):364-371. | |
| Authors: | Mei Shu-li Doctor Lu Qi-shao Professor Zhang Sen-wen Jin Li |
| Institution: | 1. College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, P.R. China 2. School of Sciences, Beijing University of Aeronautics and Astronautics, Beijing 100083, P.R. China 3. The Institute of Applied Mechanics, Jinan University, Guangzhou 510632, P.R. China |
| Abstract: | The quasi_Shannon interval wavelet is constructed based on the interpolation wavelet theory, and an adaptive precise integration method, which is based on extrapolation method is presented for nonlinear ordinary differential equations(ODEs). And then, an adaptive interval wavelet precise integration method(AIWPIM) for nonlinear partial differential equations(PDEs) is proposed. The numerical results show that the computational precision of AIWPIM is higher than that of the method constructed by combining the wavelet and the 4th Runge_Kutta method, and the computational amounts of these two methods are almost equal. For convenience, the Burgers equation is taken as an example in introducing this method, which is also valid for more general cases. |
| Keywords: | precise integration method extrapolation method Burgers equation interval wavelet |
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