The exponential asymptotic solution of differential equation
- 19 Downloads
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.
KeywordsDifferential Equation Mathematical Modeling Industrial Mathematic Asymptotic Solution Asymptotic Method
Unable to display preview. Download preview PDF.
- (1).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.Google Scholar
- (2).Day, W. B., Exponential asymptotic expansion for nonlinear differential equations, Quart. Appl. Math., Vol. 37, (1979), 169–176.Google Scholar
- (3).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.Google Scholar
- (4).Fink, P., W. S. Hall and S. Khalili, Perturbation expansion for some nonlinear wave equations, SIAM. J. Appl. Math., Vol. 24, (1973), 575–595.Google Scholar
- (5).Ting, L., Periodic solution of nonlinear wave equation in-dimensional space, SIAM. J. Appl. Math., Vol. 34, (1978), 504–514.Google Scholar
- (6).Golubeff, V. V., Analytic Theory of Differential Equation. (in Russian)Google Scholar
- (7).Milton, Van Dyke, Perturbation Mehtod in Fluid Mechanics, (1968).Google Scholar
- (8).Ting, L., Perturbation Method and Its Application in Mechanics, Lecture Notes of Institute of Mechanics, Academia Sinice, Beijing, (1980). (in Chinese)Google Scholar
- (9).Liu, C. C. and L. A. Segel, Mathematics Applied to Deterministic Problems in the Natural Science, (1974).Google Scholar
- (10).Bauer, H. F., Nonlinear response of elastic plates to pulse excitation. J. Appl. Mech., Vol. 35, (1968), 47–52.Google Scholar
- (11).Nayfeh, A. H., Perturbation Methods, (1973).Google Scholar