四阶椭圆型方程奇异摄动问题的数值解

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Numerical Solution of Singular Perturbation Problems for the Fourth-Order Elliptic Differential Equations

摘要: 本文对一类四阶椭圆型方程奇异摄动问题建立了指数型拟合差分格式,并且证明了这种格式在能量范数意义下关于小参数ε的一致收敛性.最后,我们给出了数值结果.
- 椭圆型 /
- 奇异摄动 /
- 能量范数 /
- 数值解
Abstract: In this paper we construct the finite-difference scheme for the singularly perturbed boundary value problem for the fourth-order elliptic differential equation on the basis of paper [1], and prove the uniform convergence of this scheme with respect to the small parameter e in the discrete energy norm. Finally, we give a numerical example.
- elliptic /
- singular perturbation /
- energy norm /
- numerical solution

[1]	苏坦城、刘国庆,四阶椭圆型方程奇异摄动问题渐近解,应用数学和力学,11(7) (1990),597-610.
[2]	Comstock,C,,Singular perturbations of elliptic equations I,SIAM J,Appl.Math 20 (1971),491.
[3]	Ladpzhenskaya,O,A,,The 9oundarg Problems of Mathemalical Physics,Springer-Verlag (1985).