The Study of Periodic Wavelet Based Numerical Method Applied to Burgers' Equation
Xu Bai · Journal of Jiangsu University of Science and Technology · 2001
This paper studies the numerical solution of the Galerkin projection onto a periodic wavelet basis of the Burgers partial differential equation with periodic boundary conditions.Based on the orthogonal transformation of both periodic spline wavelet within each scale and the symmetry of Burgers' equation,the nonlinerar Burgers' equation to ODEs is slmplified and the numerical solution is obtained.In phase space,an analysis is given to combinations of wavelets which represent ‘global’ functions.It is shown that the local models of the numerical solution based on periodic wavelets are more distinguishable than those of Fourier modes.This study provides a foundation for further work in which we use wavelet base to extract local models of nonlinear evolution equations.