Burgers-Fisher方程初边值问题的Chebyshev-Legendre谱方法  

Chebyshev-Legendre spectral method for the initial boundary value problem of the Burgers-Fisher equation

作　　者：郭金珠[1] 吕淑娟[1] 

机构地区：[1]北京航空航天大学数学与系统科学学院,北京100191

出　　处：《黑龙江大学自然科学学报》2016年第4期421-428,561,共8页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(11272024)

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。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.

关 键 词：BURGERS-FISHER方程 Chebyshev-Legendre谱方法 全离散格式 收敛性 

分 类 号：O241.82[理学—计算数学]