非线性对流-扩散方程初边值问题的特征-差分解法  

THE CHARACTERISTIC DIFFERENCE METHODS FOR THE NONLINEAR CONVECTION-DIFFUSION WITH INITIAL BOUNDARY CONDITION

作　　者：由同顺[1] 孙澈[1] 

机构地区：[1]南开大学

出　　处：《计算数学》1993年第2期143-155,共13页Mathematica Numerica Sinica

基　　金：国家自然科学基金

摘　　要：[1]讨论了线性方程c(x)((?u)/(?t))+b(x)(((?u)/(?x))-?/(?x))(a(x)(?u/?x))=f(x,t)初值问题的特征-有限元及特征-差分方法,[2]讨论了非线性方程 c(x)((?u)/(?t))+b(x,u)((?u)/(?x))-(?/(?x))(a(x,u)((?u)/(?x)))-f(x,u) (1.1)第一边值问题的特征-差分方法,并改善了[1]中某些重要结果。In this paper, the characteristic difference methods for the firstand the thirdboundary value problems of the nonlinear convection-diffusion equation. are conside-ved For the first boundary value problem, the L∞~ and H^1 error estimates of thecharacteristic difference schemes based on linear or quadratic interpolation arepresented. For the third boundary value problem, the L^2 and L~∞ error estimatesof the characteristic difference schemes based on linear interpolation are obtainedand a numerical example is also presented.

关 键 词：对流扩散方程 边值问题 特征差分法 

分 类 号：O241.82[理学—计算数学]