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曲边区域内对流扩散奇异摄动问题的一致差分解法

盛秦

盛秦. 曲边区域内对流扩散奇异摄动问题的一致差分解法[J]. 应用数学和力学, 1986, 7(3): 249-258.
引用本文: 盛秦. 曲边区域内对流扩散奇异摄动问题的一致差分解法[J]. 应用数学和力学, 1986, 7(3): 249-258.
Sheng Qin. Uniformly Convergent Difference Method for the Convection-Diffusion Singular Perturbation Problem in a Curved Boundary Region[J]. Applied Mathematics and Mechanics, 1986, 7(3): 249-258.
Citation: Sheng Qin. Uniformly Convergent Difference Method for the Convection-Diffusion Singular Perturbation Problem in a Curved Boundary Region[J]. Applied Mathematics and Mechanics, 1986, 7(3): 249-258.

曲边区域内对流扩散奇异摄动问题的一致差分解法

Uniformly Convergent Difference Method for the Convection-Diffusion Singular Perturbation Problem in a Curved Boundary Region

  • 摘要: 本文构造并讨论了凸曲边区域内对流扩散奇异摄动问题的差分格式及其解的一致收敛性,并证明了解的一致收敛阶为O(hββ/2)(0<β<1/2)。其中h,τ分别为空间和时间方向的网格步长。
  • [1] Тренотин В.А。,Об асимптотике решения почти линейых пароболических уравненийс параболическим погранслоем,УМН,16,1 (97) (1961),163-170.
    [2] Zlama, M,The parabolic equation as a limiting case of a certaia elliptic equation,Ann, Math.Pure, Appl,57 (1962),141-150.
    [3] Zlama, M,The parabolic equations as a limiting case of a hyperbolic and elliptic equations, Diff, Equas, and Their Appl, (Proceeding of the praque emference, 1962),Academic Press, New York (1963).
    [4] Holland, C, L,Singular perturbations in the first bountary value problems for parabolic equations, SIAM, J, Math, Anal,8, 2 (1977),268-374.
    [5] Besjes, J, G,Singular perturbation problems for linear parabolic differential operators,I, Math,48, 2 (1974),594-609.
    [6] Bobisud, L,Second-order linear parabolic equations with a small parameter, Arch,Rat, Mech, Anal,27 (1967),385-397.
    [7] Шишкин Г.И.,Разноетная ехема для решения зллиптического уравнения с малым парамстром в области с криволинсиной транинии,Ж.Вычuся.Маm.u Маm.Фuз.,18,6(1978),1466-1475.
    [8] Duffy, D, J,Uniformly convergent difference schemes for the convection-diffusion equation, Boundary and Interior Layers-Computational and Asympotic Methods, Boole Press, Dublin (1980),265-269.
    [9] 苏煜城,《奇异摄动中的边界层校正法》,上海科学技术出版社(1983).
    [10] 苏煜城、吴启光,椭圆-抛物偏微分方程奇异摄动问题的差分解法,应用数学和力学,1,2 (1980).
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出版历程
  • 收稿日期:  1985-01-24
  • 刊出日期:  1986-03-15

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