On certain properties of linear iterative equations

Jean-Claude Ndogmo; Fazal Mahomed

Open Mathematics (2014)

  • Volume: 12, Issue: 4, page 648-657
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Jean-Claude Ndogmo, and Fazal Mahomed. "On certain properties of linear iterative equations." Open Mathematics 12.4 (2014): 648-657. <http://eudml.org/doc/269743>.

@article{Jean2014,
abstract = {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.},
author = {Jean-Claude Ndogmo, Fazal Mahomed},
journal = {Open Mathematics},
keywords = {Linear iterative equation; Recurrence relations; Canonical form; Coefficients characterization; Normal form; linear iterative equations; recurrence relations; canonical form; coefficients characterization; normal form},
language = {eng},
number = {4},
pages = {648-657},
title = {On certain properties of linear iterative equations},
url = {http://eudml.org/doc/269743},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Jean-Claude Ndogmo
AU - Fazal Mahomed
TI - On certain properties of linear iterative equations
JO - Open Mathematics
PY - 2014
VL - 12
IS - 4
SP - 648
EP - 657
AB - 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.
LA - eng
KW - Linear iterative equation; Recurrence relations; Canonical form; Coefficients characterization; Normal form; linear iterative equations; recurrence relations; canonical form; coefficients characterization; normal form
UR - http://eudml.org/doc/269743
ER -

References

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  9. [9] Ndogmo J.C., Equivalence transformations of the Euler-Bernoulli equation, Nonlinear Anal. Real World Appl., 2012, 13(5), 2172–2177 http://dx.doi.org/10.1016/j.nonrwa.2012.01.012 Zbl1257.35006
  10. [10] Ndogmo J.C., Some results on equivalence groups, J. Appl. Math., 2012, #484805 Zbl1280.34041
  11. [11] Schwarz F., Solving second order ordinary differential equations with maximal symmetry group, Computing, 1999, 62(1), 1–10 http://dx.doi.org/10.1007/s006070050009 Zbl0934.34001
  12. [12] Schwarz F., Equivalence classes, symmetries and solutions of linear third-order differential equations, Computing, 2002, 69(2), 141–162 http://dx.doi.org/10.1007/s00607-002-1454-0 Zbl1025.34005
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