Approximation of Periodic Solutions of a System of Periodic Linear Nonhomogeneous Differential Equations
Tóm tắt
The present paper does not introduce a new approximation but it modifies a certain known method. This method for obtaining a periodic approximation of a periodic solution of a linear nonhomogeneous differential equation with periodic coefficients and periodic right-hand side is used in technical practice. However, the conditions ensuring the existence of a periodic solution may be violated and therefore the purpose of this paper is to modify the method in order that these conditions remain valid.
Tài liệu tham khảo
N. K. Bobylev, J. K. Kim, S. K. Korovin et al.: Semidiscrete approximation of semilinear periodic problems in Banach spaces. Nonlinear Anal. 33 (1998), 473-482.
B. M. Budak, S. V. Fomin: Multiple Integrals and Series. Nauka, Moskva, 1971. (In Russian.)
E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations. McGraw-Hill, New York-Toronto-London, 1955.
P. Hartman: Ordinary Differential Equations. John Wiley & Sons, New York-London-Sydney, 1964.
V. N. Laptinskij: Fourier approximations of periodic solutions of nonlinear differential equations. Differ. Equ. 21 (1985), 1275-1280.
L. A. Liusternik, V. J. Sobolev: Elements of Functional Analysis. Nauka, Moskva, 1965. (In Russian.)
I. G. Main: Vibrations and Waves in Physics. Cambridge University Press, 1978, 1984, pp. 89-97.
S. Timoshenko, D. H. Young: Advanced Dynamics. Mc Graw-Hill, New York-Toronto-London, 1948.
L. Q. Zhang: Spline collocation approximation to periodic solutions of ordinary differential equations. J. Comput. Math. 10 (1992), 147-154.
L. Q. Zhang: Two-sided approximation to periodic solutions of ordinary differential equations. Numer. Math. 66 (1993), 399-409.