对流扩散方程的全离散Legendre和Chebyshev谱方法  

Fully discrete Legendre and Chebyshev spectral methods for advection-diffusion equations

作　　者：崔鸿玉 张法勇[1] CUI Hongyu;ZHANG Fayong(School of Mathematical Sciences,Heilongjiang University,Harbin 150080,China)

机构地区：[1]黑龙江大学数学科学学院,哈尔滨150080

出　　处：《黑龙江大学自然科学学报》2018年第6期662-670,共9页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10371077)

摘　　要：用Legendre和Chebyshev谱方法对一维对流扩散方程的初边值问题{ut-νuxx+(bu)x+b0u=f(x,t),x∈Λ,t∈J,u(±1,t)=0,t∈J,u(x,0)=u0(x),x∈Λ。进行数值分析,研究全离散的Euler隐格式,证明Euler隐格式的稳定性,得到近似解的收敛性及与精确解之间的误差估计。The initial boundary value problem of one-dimensional convection diffusion equation{ut-νuxx+( bu)x+ b0 u = f( x,t),x ∈ Λ,t ∈ J,u( ± 1,t) = 0,t ∈ J,u( x,0) = u0( x),x ∈ Λ.is numerically analyzed by using the Legendre and Chebyshev spectral methods. The fully discretized Euler implicit scheme is studied. The stability of the Euler implicit scheme is proved. Finally,the convergence of the approximate solution and the error estimate between the solution and the exact solution are obtained.

关 键 词：对流扩散方程 Chebyshev谱方法 LEGENDRE谱方法 稳定性 收敛性 

分 类 号：O241.82[理学—计算数学]