求解对流扩散方程的Haar小波方法

本文用Haar小波求解对流扩散方程，将满足初始和边界条件的常系数偏微分方程简化为较简单的代数方程组进行求解．实例说明了这种方法具有收敛速度快和计算容易的特点，同时又避免了用Daubechies小波求解微分方程需要计算相关系数的麻烦．本文所使用的方法可以求解一般的微（积）分方程．

Haar Wavelet Method for Solving the Convection-diffusion Equation

An operational matrix of integration based on the Haar wavelet is established,and the procedure for applying the matrix to solve the one-dimensional convection-diffusion equation with constant coefficients which satisfies the boundary conditions and initial condition is formulated.The fundamental idea of Haar wavelet method is to convert the partial differential equation into a group of algebra equations which involves a finite number of variables.The example is given to demonstrate the fast and flexible of the method,in the mean time,it is found that the trouble of Daubechies wavelets for solving the differential equation which need to calculate the correlation coefficients is avoided.The method can be used to deal with all the other differential and integral equations.