On the Approximate Lie Symmetries of Differential Equations
by
Mehmet Can
International University of Sarajevo, Faculty of Arts and Social Sciences, Paromlinska 66, Sarajevo, Bosnia and Herzegovina

Abstract

To P. G. L. Leach, the concept of an approximate symmetry goes back to the late seventies. Since the differential equations which arise in mathematical modeling are invariably approximate, one should expect that the symmetries would also approximate. A concept of approximate symmetry of a differential equation with a small parameter and algorithm of calculating such symmetries were proposed first by V.A. Baikov et.al. in 1989. Examples of the approximate symmetries show that such symmetries usually do not form Lie algebra, but form a so-called approximate Lie algebra in sense of definition given by the same authors in 1993. Then W. I. Fushchych and W. M. Shtelen introduced a different concept of approximate symmetries also in 1989. Then M. Pakdemirli et. al. in 2001 compared two previous approximate symmetry concepts an proposed a new one. In this article a new concept of approximate symmetry will be searched which will be approximate as in the sense of V.A. Baikov et. al. and will lead approximate solutions as in M. Pakdemirli et. al. in 2001.

Date received: March 13, 2008