A Uniformly Convergent Difference Scheme for the Singular Perturbation Problem of a High Order Elliptic Differential Equation

Liu Guoqing; Su Yucheng

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Article Navigation > Applied Mathematics and Mechanics > 1996 > 17(5): 397-404

Liu Guoqing, Su Yucheng. A Uniformly Convergent Difference Scheme for the Singular Perturbation Problem of a High Order Elliptic Differential Equation[J]. Applied Mathematics and Mechanics, 1996, 17(5): 397-404.

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A Uniformly Convergent Difference Scheme for the Singular Perturbation Problem of a High Order Elliptic Differential Equation

Liu Guoqing¹,
Su Yucheng²

1.
Nanjing Institute of Chemical Technolngy, Nanjing 210009, P. R. China;
2.
Nanjing University, Nanjing 210008, P. R. China

Received Date: 1995-04-28
Publish Date: 1996-05-15

Abstract

Abstract

In this paper, we first consider the singularly perturbed boundary value problem for the fourth-order elliptic differential equation, establish the priori estimation of the solution of the continuous problem. Then, we present an exponential fitted difference scheme and discuss the solution properties of the difference equations. Finally, the uniform convergence of this scheme with respect to the small parameter in the discrete energy norm, is proved.
- elliptic,
- singular perturbation,
- difference scheme,
- uniform convergence

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References(6)

References

[1]	O.A.Ladyzhenskaya,The Boundary Problems of Mathematical Physics,Springer-Verlag (1985).
[2]	K.Niijima,A uniformly convergent difference scheme for a semilinear singular perturbation problem,Numer.Math.,43 (1984) 175-198.
[3]	苏爆城,《奇异摄动中的边界层校正法》,上海科技出版社(1983).
[4]	苏爆城、吴启光,《奇异摄动问题数值方法引论》,重庆出版社(1991).
[5]	苏湿城、刘国庆,四阶椭圆型奇异摄动问题渐近解,应用数学和力学,11(7) (1990),597-610,
[6]	苏煌城、刘国庆,四阶椭圆型奇异摄动问题的数值解,应用数学和力学,12(10) (1991),879-901