偏微分方程的区间小波自适应精细积分法

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．

Adaptive Interval Wavelet Precise Integration Method for Partial Differential Equations

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.