守恒型自共轭奇摄动常微分方程一致收敛二阶格式

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A Uniformly Convergent Second Order Difference Scheme for a Singularly Perturbed Self-Adjoint Ordinary Differential Equation in Conservation Form

摘要: 本文对守恒型自共轭奇异摄动常微分方程,利用El-Mistikawy和Werle^[1]的思想构造一个差分格式,并证明该格式为关于ε一致收敛的二阶格式.

Abstract: In this paper, based on the idea of El-Mistikawy and Werle we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme.

[1]	El-Mistikawy,T.M.and M.J.Werle,Numerical method for boundary layers with blowing the exponential box scheme,AIAA.J.,16(1978) 749-751.
[2]	Hegarty,A.F.,J.J.H.Miller and E.O'Riordan,Uniform second order difference scheme for singular perturbation problems,Proc.Internat.Conf on Boundary and Interior Layers,Computational and Asymptotic Methods,June 3-6(1980),Trinity College,Dublin,Ireland(J.J.H.Miller ed.),Boole Press,Dublin(1980),301-305.
[3]	郭雯,小参数自共辆问题Ezpoaentlal Box格式的一致收敛性,国际常微分方程会议资料,福州大学(1985).
[4]	Smith,D.R.,The multivariable method in singular perturbation analysis,SIAM Rev.,17(1973),221-273.

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