奇异摄动问题的一类变分差分格式

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A Class of Variational Difference Schemes for a Singular Perturbation Problem

摘要: 本文讨论了奇异摄动二阶自伴常微分方程边值问题,采用有限元方法构造了一类变分差分格式,在对系数的光滑性假定很弱的情况下证明了一致收敛性.这类格式包括了[1],[3],[4]和[5]中讨论的格式.

Abstract: In this paper, a singularly perturbed boundary value problem for second order self-adjoint ordinary differential equation is discussed.A class of variational difference schemes is constructed by the finite element method.Uniform convergence about small parameter is proved under a weaker smooth condition with respect to the coefficients of the equation.The schemes studied in refs.[1], [3], [4] and [5] belong to the cllass.

[1]	Hegarty,A.F.,J,J,H, Miller and E, O'Riordan,Uniform second order difference schemes for singular perturbation problems, Boundary and Interior Layers-Computational and Asymptotic Methods (J.J. H.Miller ed,),Boole Przss, Dublin (1980), 301-305.
[2]	El-Mistikawy,T.M. and M. J.Werle,Numerical method for boundary layers with blowing-The exponential box scheme, AIAA T.,16 (1978),749-751.
[3]	Niijima, K.,An error analysis of some difference method for a singular perturbation problem, Mem, Numer, Math.,8-9 (1981/1982), 1-19.
[4]	Niijima.K.,On a three-point difference scheme for a singular perturbation problem without a first derivative term, Ⅰ,Mem.Numer, Math.,7 (1980),1-10.
[5]	Niijima, K.,On a three-point difference scheme for a singular perturbation problem without a first derivative term, Ⅱ,Mem. Numer, Math.,7 (1980),11-27.
[6]	Boglaev,I.P.,A variational difference scheme for a boundary value problem with a small parameter in the highest derivative, U,S.S,R, Comput.Math.and Math,Phys.21, 4 (1981), 71-81.
[7]	林平,一些奇异摄动问题的数值解,南京大学数学系硕士论文,南京(1987).
[8]	林平,自伴常微分方程奇异摄动边值问题的二阶一致收敛差分格式,南京大学学报数学半年刊 (待发表).