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

Sheng Qin

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Article Navigation > Applied Mathematics and Mechanics > 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.

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.

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

Sheng Qin

Suzhou University, Suzhou

Received Date: 1985-01-24
Publish Date: 1986-03-15

Abstract

Abstract

In this paper we construct a difference scheme for the convection-diffusion.singular perturbation problem in a convex curved boundary region, and discuss the uniform convergence of its solution. We have proved that the, order of uniform convergence of its solution is O(h^β+τ^β/2)(0<β<1/2),where h,τ are the mesh steps in the space and time directions respectively.

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References(10)

References

[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).