Su Yu-cheng, Shen Quan. The Numerical Solution of a Singularly Perturbed Problem for Quasilinear Parabolic Differential Equation[J]. Applied Mathematics and Mechanics, 1992, 13(6): 479-488.
Citation: Su Yu-cheng, Shen Quan. The Numerical Solution of a Singularly Perturbed Problem for Quasilinear Parabolic Differential Equation[J]. Applied Mathematics and Mechanics, 1992, 13(6): 479-488.

The Numerical Solution of a Singularly Perturbed Problem for Quasilinear Parabolic Differential Equation

  • Received Date: 1991-07-25
  • Publish Date: 1992-06-15
  • We consider the numerical solution of a singularly perturbed problem for the quasilinear parabolic differential equation,we construct a linear three-level finite difference scheme on a nonuniform grid.The uniform convergence in the sense of discrete L2 norm is proved and numerical examples are presented.
  • loading
  • [1]
    Oleinik,O.A.and T.D.Ventcel,The first boundary problem and the Cauchy problem for quasi-linear equations of parabolic type,Mat.Sb.N.S.,41,83(1957),105-128.
    [2]
    Vishik,M.I.and L.A.Lyusternik,Regular degeneration and boundary layer for linear differential equations with small parameter,Usp.Mat.Nauk,12(1957),3-122.
    [3]
    苏煌城.《奇异摄动中的边界层校正法》.上海科技出版社(1983).
    [4]
    Trenogin,V.A.,On the asymptotic character of solutions of near-linear parabolic equations with a parabolic boundary layer,Usp.Mat.Nauk,16,1(1961).163-169.
    [5]
    Bakhvalov,N.S.,On the optimization of the methods for solving boundary value problems in the presence of a boundary layer,Zh.Vychisl.Mat.i Mat.Fiz.,9(1969),841-859.
    [6]
    Shishkin,G.I.,Solution of a boundary value problem for an elliptic equation with small parameter multiplying the highest derivatives,ibid,86,7(1986),1019-1031.
    [7]
    Vulanovic,R.,On a numerical solution of a type of singularly perturbed boundary value problem by using a special discretization mesh,Zb.rad.Prir-mat.Fak.Univ.u Novom Sadu,Ser.Mat.,13(1983),187-201.
    [8]
    Lees,M.,A linear three-level difference scheme for quasilinear parabolic equation,Math.Comp.,20(1966),516-522.
    [9]
    戴伟忠、陈传淡.二维非线性抛物型微分方程的一个三层差分格式,计算数学,11(1)(1989)1-9.
    [10]
    Meck,P.C.and J.Norbury,Two-stage,two-level finite difference schemes for non-linear parabolic equations,IMA J.Numer.Anal.,2(1982),335-370.
    [11]
    萨马尔斯基、安德烈耶夫,《椭圆型方程差分方法》(中译本),科学出版社(1984).
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1872) PDF downloads(507) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return