A perturbation method based on integrating factors

被引：18

作者：

Van Horssen, WT ^{[1
]}

机构：

[1] Delft Univ Technol, Dept Tech Math & Informat, NL-2628 CD Delft, Netherlands

来源：

SIAM JOURNAL ON APPLIED MATHEMATICS | 1999年 / 59卷 / 04期

关键词：

integrating factor; exact differential equations; integrating vector; first integrals; perturbation method; asymptotic approximation of first integral; existence and stability of time-periodic solution;

D O I：

10.1137/S0036139996309151

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper it will be shown that all integrating factors for a system of n first-order, ordinary differential equations have to satisfy a system of 1/2 n(n + 1) first-order, linear partial differential equations. A perturbation method based on integrating factors will be presented for problems containing a small parameter. When approximations of integrating factors have been obtained an approximation of a first integral (including an error estimate) can be given. To show how this perturbation method works the method is applied to the Van der Pol equation, a forced Duffing equation, and a perturbed Volterra-Lotka system. Not only will asymptotic approximations of first integrals be given, but it will be shown how, in a rather efficient way, the existence and stability of time-periodic solutions can be obtained from these approximations.

引用

页码：1427 / 1443

页数：17