偏微分方程的区间小波自适应精细积分法

基金项目: 国家自然科学基金资助项目(10372036;10172011)

Adaptive Interval Wavelet Precise Integration Method for Partial Differential Equations

1.
College of Information and Electrical Engineering, China Agricultural University, Beijing 100083, P. R China;
School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, P. R. China;

摘要: 利用插值小波理论构造了拟Shannon区间小波，并结合外推法给出了一种求解非线性常微分方程组的时间步长自适应精细积分法，在此基础上构造了求解非线性偏微分方程的区间小波自适应精细积分法（AIWPIM）．数值结果表明，该方法在计算精度上优于将小波和四阶Runge-Kutta法组合得到的偏微分方程的数值求解方法，而计算量则相差不大．该文方法通过Burgers方程给出，但适用于一般情形．
- 精细积分法 /
- 外推法 /
- Burgers方程 /
- 区间小波
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 ODEs. And then, an adaptive interval wavelet precise integration method (AIWPIM) for nonlinear 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.
- precise integration method /
- extrapolation method /
- Burgers equation /
- interval wavelet

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