| Title:
|
Approximation of periodic solutions of a system of periodic linear nonhomogeneous differential equations (English) |
| Author:
|
Fischer, Alexandr |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
49 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
269-284 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
oscillation problem |
| Keyword:
|
periodic differential equation |
| Keyword:
|
periodic solution |
| Keyword:
|
$\omega $-periodic solution |
| Keyword:
|
trigonometric polynomial |
| Keyword:
|
trigonometric approximation |
| Keyword:
|
Gram’s determinant |
| MSC:
|
34A45 |
| MSC:
|
34C25 |
| MSC:
|
42A10 |
| idZBL:
|
Zbl 1099.34041 |
| idMR:
|
MR2059430 |
| DOI:
|
10.1023/B:APOM.0000042366.62321.55 |
| . |
| Date available:
|
2009-09-22T18:18:07Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134569 |
| . |
| Reference:
|
[1] 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. MR 1635712, 10.1016/S0362-546X(97)00560-9 |
| Reference:
|
[2] B. M. Budak, S. V. Fomin: Multiple Integrals and Series.Nauka, Moskva, 1971. (Russian) MR 0349912 |
| Reference:
|
[3] E. A. Coddington, N. Levinson: Theory of Ordinary Differential Equations.McGraw-Hill, New York-Toronto-London, 1955. MR 0069338 |
| Reference:
|
[4] P. Hartman: Ordinary Differential Equations.John Wiley & Sons, New York-London-Sydney, 1964. Zbl 0125.32102, MR 0171038 |
| Reference:
|
[5] V. N. Laptinskij: Fourier approximations of periodic solutions of nonlinear differential equations.Differ. Equ. 21 (1985), 1275–1280. Zbl 0617.34032, MR 0818569 |
| Reference:
|
[6] L. A. Liusternik, V. J. Sobolev: Elements of Functional Analysis.Nauka, Moskva, 1965. (Russian) MR 0209802 |
| Reference:
|
[7] I. G. Main: Vibrations and Waves in Physics.Cambridge University Press, 1978, 1984, pp. 89–97. |
| Reference:
|
[8] S. Timoshenko, D. H. Young: Advanced Dynamics.Mc Graw-Hill, New York-Toronto-London, 1948. MR 0028707 |
| Reference:
|
[9] L. Q. Zhang: Spline collocation approximation to periodic solutions of ordinary differential equations.J. Comput. Math. 10 (1992), 147–154. Zbl 0776.65051, MR 1159628 |
| Reference:
|
[10] L. Q. Zhang: Two-sided approximation to periodic solutions of ordinary differential equations.Numer. Math. 66 (1993), 399–409. Zbl 0799.65077, MR 1246964, 10.1007/BF01385704 |
| . |
