Construction of quasi-periodic solutions of guaranteed accuracy by the small parameter method

Kh. I. Botashev

State Academy of Agriculture, ul. Tarchokova 1a, Nalchik, Kabardino-Balkariya, 360030, Russia

Abstract: Theorems on the localization of exact solutions are proved for a quasilinear mathematical model describing quasi-periodic processes. Based on these theorems, constructive algorithms are proposed for calculating quasi-periodic solutions with guaranteed accuracy. Quasi-periodic motions play an important role in engineering and physics, where they often represent determining states. Quasi-periodic motions can be found in many ecological, biological, and economic processes.

Key words: system of first-order ordinary differential equations, the case of a small parameter, quasiperiodic solutions, guaranteed accuracy.

UDC: 519.624.2

Received: 13.05.2005
Revised: 05.08.2005

 English version: Computational Mathematics and Mathematical Physics, 2006, 46:1, 90–96

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