A perturbative algorithm for quasi-periodic linear systems close to constant coefficients

被引：2
作者：
Arnal, Ana
Casas, Fernando [1 ]
Chiralt, Cristina
机构：
[1] Univ Jaume 1, Inst Matemat & Aplicac Castello, E-12071 Castellon de La Plana, Spain
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 273卷
关键词：
Perturbation algorithm; Quasi-linear differential equations; Stability analysis; DIFFERENTIAL-EQUATIONS; REDUCIBILITY;
D O I：
10.1016/j.amc.2015.10.012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A perturbative procedure is proposed to formally construct analytic solutions for a linear differential equation with quasi-periodic but close to constant coefficients. The scheme constructs the necessary linear transformations involved in the reduction process up to an arbitrary order in the perturbation parameter. It is recursive, can be implemented in any symbolic algebra package and leads to accurate analytic approximations sharing with the exact solution important qualitative properties. This algorithm can be used, in particular, to carry out systematic stability analyses in the parameter space of a given system by considering variational equations. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：398 / 409
页数：12
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