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拟线性抛物型方程奇异摄动问题的数值解法

苏煜城 沈全

苏煜城, 沈全. 拟线性抛物型方程奇异摄动问题的数值解法[J]. 应用数学和力学, 1992, 13(6): 479-488.
引用本文: 苏煜城, 沈全. 拟线性抛物型方程奇异摄动问题的数值解法[J]. 应用数学和力学, 1992, 13(6): 479-488.
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.

拟线性抛物型方程奇异摄动问题的数值解法

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

  • 摘要: 本文讨论拟线性抛物型方程奇异摄动问题的差分解法,在非均匀网格上建立了线性三层差分格式,并证明了在离散的L2范数意义下格式的一致收敛性,最后给出了一些数值例子.
  • [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).
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出版历程
  • 收稿日期:  1991-07-25
  • 刊出日期:  1992-06-15

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