一类二阶微分差分方程边值问题的奇摄动解
Singular Perturbation Solution of Boundary-Value Problem for a Second-Order Differential-Difference Equation
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摘要: 本文利用两变量展开直接构造边界层项的方法,讨论了一类二阶微分差分方程边值问题的奇摄动解,构造了形式渐近解,作出了余项估计,从而证明了解的存在性.Abstract: It this paper, the method of two-variables expansion is used to construct boundary layer terms of asymptotic solution of the boundary-value problem for a second-order DDE. The n-order formal asymptotic solution is obtained and the error is estimated. Thus the existence of uniformly valid asymptotic solution is proved.
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[1] Lange, C.G. and R.M. Miura, Singular perturbation analysis of boundary value problem for differential-difference equation, SIMA J. Appl. Math., 42,3 (1982), 502-531. [2] Nayfeh, A.H., Perturbation methods. Ist ed. New York, John Wiley and Sons (1973). [3] 江福汝,关于边界层方法,应用数学和力学,2, 5 (1981), 461-474. [4] 江福汝,关于椭圆型方程的奇摄动,复旦大学学报(自然科学版),2(1978),29-37. [5] Murray, H.P. and F.W. Hams. Maximum Principles in Differential Equation, Prentice-Hall, Englewood Cliffs, New Jersey, (1967). [6] Chang, K.W. and F.A. Howes, Nonlinear Singular Perturbation Phenomena: Theory and Application, lst ed. New York, Springer-Verlag (1984). [7] O'Malley, R.E., Introduction to Singular Perturbations. lst ed., New York, Academic Press (1974). [8] Xu Jun-tao. Singular perturbation of boundary-value problem for a second-order differentialdiference equation. Ann. of Diff. Eqs., 2, 1 (1986), 47-64. -
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