中文摘要：

用Chebyshev-Legendre谱方法对Burgers-Fisher方程的初边值问题构造全离散线性逼近格式,通过直接对近似解与精确解之间的误差估计,证明离散格式的收敛性,得到在L2范数和H1范数意义下误差的最优阶估计。数值算例验证了算法的有效性和结果的正确性。

英文摘要：

By using the so-called Chebyshev-Legendre spectral method, a fully discrete linear approxima- tion scheme for the initial boundary value problem of the Burgers-Fisher equation is constructured. The convergence of the scheme is proved by estimating the error between the approximate solution and exact solution. The optimal order estimation of the error is given in the sense of the L2 norm and H1 norm. A numerical example is presented to illustrate the effectiveness of algorithm and correction of results.