On certain properties of linear iterative equations

被引：4

作者：

Ndogmo, Jean-Claude ^{[1
]}

Mahomed, Fazal M. ^{[2
]}

机构：

[1] Univ Witwatersrand, Sch Math, ZA-2050 Johannesburg, South Africa

[2] Univ Witwatersrand, Sch Computat & Appl Math, Ctr Differential Equat Continuum Mech & Applicat, ZA-2050 Johannesburg, South Africa

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2014年 / 12卷 / 04期

关键词：

Linear iterative equation; Recurrence relations; Canonical form; Coefficients characterization; Normal form; ORDINARY DIFFERENTIAL-EQUATIONS;

D O I：

10.2478/s11533-013-0364-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

An expression for the coefficients of a linear iterative equation in terms of the parameters of the source equation is given both for equations in standard form and for equations in reduced normal form. The operator that generates an iterative equation of a general order in reduced normal form is also obtained and some other properties of iterative equations are established. An expression for the parameters of the source equation of the transformed equation under equivalence transformations is obtained, and this gives rise to the derivation of important symmetry properties for iterative equations. The transformation mapping a given iterative equation to the canonical form is obtained in terms of the simplest determining equation, and several examples of application are discussed.

引用

页码：648 / 657

页数：10

共 14 条

[1] Superposition rules for higher order systems and their applications [J].