周期小波基下Burgers方程数值模拟

研究周期边界条件下非线性Burgers方程的周期小波基下Galerkin解 利用周期样条小波基的正交变换 ,结合Burgers方程所具有的对称性作线性变换 ,约化非线性Burgers方程为一组常微分方程组 ,得到该方程的Galerkin解 ,在相空间中进行分析 ,采用能表征全域特性的小波组合函数 ,数值分析表明周期小波基下Galerkin解与Fourier分析下的数值解比较更能反映方程的局部特征 本文的研究为非线性发展方程的局部复杂性研究提供了一个新的基础

The Study of Periodic Wavelet Based Numerical Method Applied to Burgers' Equation

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.