Model reduction of spatiotemporal systems using quasi-Shannon interval wavelet

A novel model reduction technology using wavelet-collocation method is presented to apply to the spatiotemporal systems. First, contrasting Daubechies wavelet bases, quasi-Shannon interval wavelet is presented as the basis functions in order to preserve the distinctive local property of wavelet, and overcome the computation of connection coefficient and the border effect; Then, the spatiotemporal systems are divided into finite-dimensional ordinary differential equations by the afore-mentioned basis functions, and after that the notation of the finite difference methods in time domain are performed to get the satisfying simplified model. In final, a steep Burgers equation is explained as example to demonstrate the effectiveness of the proposed method.