奇异摄动问题的一类非完全指数拟合差分格式

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A Class of Incompletely Exponentially Fitted Difference Schemes for a Singular Perturbation Problem

摘要: 本文分析奇异摄动问题εu"+a(x)u'-b(x)u=f(x),0a>0,b(x)≥0的一类非完全指数拟合差分格式一致收敛阶的充分条件,由此构造出二阶一致收敛的非完全指数拟合差分格式,最后给出数值结果.

Abstract: Some sufficient conditions are considered, under which the solutions of a class of incompletely exponentially fitted difference schemes converge uniformly in e, with orders one and two, to the solution of the singular perturbation problem: eu"+a(x)u'-b(x)u=f(x), for 0a>0, b(x)≥0. From these conditions.an incompletely exponentially fitted second-order scheme is derived. Finally, the results of some numerical experiments are given.

[1]	Lorenz,J.,Stability and consistency analysis of difference methods for singular perturbation problems,Proc.Conf.on Analytical and Numerical Approaches to Asymptotic Problems in Analysis,June(1980),9-13,University of Nijmegen,The Netherlands(O.Axelsson,L.Frank and A.Van der Sluis,Eds.)North-Holland,Amsterdam(1981).
[2]	Doolan,E.P.,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers,Boole Press,Dublin(1980).
[3]	林鹏程、孙光甫,奇异摄动问题的完全指数拟合差分格式.(待发表)
[4]	Varga,R.S.,Matrix Iterative Analysis,Prentice-Hall,Englewood Cliffs,N.J.(1962).

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