×

A special case of the successive approximation method for autonomous differential equations with a small parameter. (English) Zbl 1096.34507

Differ. Equ. 41, No. 3, 429-432 (2005); translation from Differ. Uravn. 41, No. 3, 408-410 (2005).
The successive approximation method is used to approximate the solution of a nonlinear autonomous differential equation with a small parameter.

MSC:

34A45 Theoretical approximation of solutions to ordinary differential equations
34D10 Perturbations of ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Volosov, V.M. and Morgunov, B.I., Metod osredneniya v teorii nelineinykh kolebatel’nykh sistem (Averaging Method in Theory of Nonlinear Oscillation Systems), Moscow, 1971. · Zbl 0232.70021
[2] Bogolyubov, N.N. and Mitropol’skii, Yu.A., Asimptoticheskie metody v teorii nelineinykh kolebanii (Asymptotic Methods in Theory of Nonlinear Oscillations), Moscow, 1974. · Zbl 0303.34043
[3] Moiseev, N.N., Asimptoticheskie metody nelineinoi mekhaniki (Asymptotic Methods of Nonlinear Mechanics), Moscow, 1981. · Zbl 0527.70024
[4] Pontryagin, L.S., Obyknovennye differentsial’nye uravneniya (Ordinary Differential Equations), Moscow, 1982. · Zbl 0526.34001
[5] Cesari, L., Asymptotic Behavior and Stability Problems in Ordinary Differential Equations, Berlin, 1959. Translated under the title Asimptoticheskoe povedenie i ustoichivost’ reshenii obyknovennykh differentsial’nykh uravnenii, Moscow, 1964.
[6] Kuz’mina, R.P., Metod malogo parametra v regulyarno vozmushchennoi zadache Koshi (Method of Small Parameter in a Regularly Perturbed Cauchy Problem), Moscow, 1991.
[7] Kuz’mina, R.P., Differents. Uravn., 1987, vol. 23, no.2, pp. 352–353.
[8] Goroshchenya, A.B. and Vesnina, A.A., Vvedenie v asimptoticheskie metody teorii differentsial’nykh uravnenii (Introduction to Asymptotic Methods in Theory of Differential Equations), Omsk, 1975.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.