Abstract
In this paper, the exponential asymptotic solution (E.A.S.) of differential equation is discussed. Firstly, E.A.S. of the second-order differential equation is studied and the orthogonal conditions of the uniformly valid E.A.S. are found out. Next, E.A.S. in matched asymptotic method is discussed. Finally, some examples are given.
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References
Brull, M. A. and A. I. Soler, A new porturbation technique for differential equations with small parameter, Quart. Appl. Math., Vol. 24, (1966), 143–151.
Day, W. B., Exponential asymptotic expansion for nonlinear differential equations, Quart. Appl. Math., Vol. 37, (1979), 169–176.
Keller, J. B. and L. Ting, Periodic vibrations of systems governed by nonlinear partial differential equations, Comm. Pure Appl. Math., Vol. 19, (1966), 371–420.
Fink, P., W. S. Hall and S. Khalili, Perturbation expansion for some nonlinear wave equations, SIAM. J. Appl. Math., Vol. 24, (1973), 575–595.
Ting, L., Periodic solution of nonlinear wave equation in-dimensional space, SIAM. J. Appl. Math., Vol. 34, (1978), 504–514.
Golubeff, V. V., Analytic Theory of Differential Equation. (in Russian)
Milton, Van Dyke, Perturbation Mehtod in Fluid Mechanics, (1968).
Ting, L., Perturbation Method and Its Application in Mechanics, Lecture Notes of Institute of Mechanics, Academia Sinice, Beijing, (1980). (in Chinese)
Liu, C. C. and L. A. Segel, Mathematics Applied to Deterministic Problems in the Natural Science, (1974).
Bauer, H. F., Nonlinear response of elastic plates to pulse excitation. J. Appl. Mech., Vol. 35, (1968), 47–52.
Nayfeh, A. H., Perturbation Methods, (1973).
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Communicated by Xu Sheng-fen
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Zheng-rong, L., Jun-tao, X. The exponential asymptotic solution of differential equation. Appl Math Mech 5, 1255–1262 (1984). https://doi.org/10.1007/BF01895121
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DOI: https://doi.org/10.1007/BF01895121