PLK方法适用性的研究
The Study of Applicability for PLK Method
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摘要: 本文基于Π-U理论,对PLK方法应用于奇异摄动问题的适用性进行了研究,给出了形式渐近解的一般公式和应用PLK方法的必要性条件,并举例对本文的方法的应用进行了讨论,Abstract: This paper researches the applicability of the PLK method. We give the general formulae of the asymptotic solution and strained coordinates, and we establish necessary conditions for the applicability PLK method. Besides, the applicability of the approach is also exemplified by means of examples in this paper.
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[1] Nayfcn,A.H.,Perturbation Methods,John Wiley,New York,Ch.3(1973). [2] Wasow,W.A.,On the convergence of an approximation method of M.J.Lighthill,J.Rational Mech.Anal.,4(1955),751-767. [3] Usher,P.D.,Necessary conditions for applicability of Poincar-Lighthill perturbation theory,Quart.Appl.Math.,28(1971),463-471. [4] Comstock,C.,On Lighthill's method of strained coordinates,SIAM J.Appl.Math.,16(1968),596-602. [5] Pritulo,M.F.,On the determination of uniformly accurate solutions of differential equations by the method of perturbation of coordinates,J.Appl.Math.Mech.,26(1962).661-667. [6] Usher,P.D.,Coordinate stretching and interface,location Ⅱ,a new PL expansion,J.Computational Phys.,29,3(1978),29-39. [7] Jordan,D.W.and P.Smith.Nonlinear Ordinary Differential Equations,Clarendon Press,Oxford(1977),152-155． -
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