Symmetry and transformation properties of linear iterative ordinary differential equation
Date
2013-08-06
Authors
Folly-Gbetoula, Mensah Kekeli
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Abstract
Solutions of linear iterative equations and expressions for these solutions in terms of
the parameters of the source equation are obtained. Based on certain properties of iterative
equations, nding the solutions is reduced to nding group-invariant solutions
of the second-order source equation. We have therefore found classes of solutions
to the source equations. Regarding the expressions of the solutions in terms of the
parameters of the source equation, an ansatz is made on the original parameters r
and s, by letting them be functions of a speci c type such as monomials, functions of
exponential and logarithmic type. We have also obtained an expression for the source
parameters of the transformed equation under equivalence transformations and we
have looked for the conservation laws of the source equation. We conducted this
work with a special emphasis on second-, third- and fourth-order equations, although
some of our results are valid for equations of a general order.
Description
A dissertation submitted to the Faculty of Science, University of the Witwatersrand,
Johannesburg, in fulflment of the requirements for the degree of Master of science.
Johannesburg, December 2012.