广义Burgers-Fisher方程的Haar小波有限差分法

研究了基于Haar小波有限差分法求解广义Burgers-Fisher方程.给出Haar小波族的定义,建立积分运算矩阵,该矩阵把积分运算转化为矩阵运算.对方程时间方向的离散采用向前差商,空间方向的离散采用Haar小波.利用Haar矩阵的稀疏性,有效地提高了计算速度和精度.通过计算机模拟获得数值结果,并与Adomian分解法进行比较,结果显示本文所给出的方法对求解时间较小问题时优于Adomian分解法.

Haar wavelet finite difference method for solving the generalized Burgers-Fisher equation

A solution of the generalized Burgers-Fisher equation based on the Haar wavelet finite difference method is studied.The Haar wavelet family is given.The operational matrix of integration is established.The matrix is to convert the integral operations into the matrix operations.According to this method,the spatial operators are approximated by the Haar wavelet and the time derivation operators by the forward difference quotient.This method improves the computation speed and accuracy due to the sparsity of the Haar matrices.Numerical results,obtained by computer simulation,are compared with the Adomian decomposition method.The result shows that the method for solving problems of short time is better than Adomian decomposition method.