On a new method for finding generalized equivalence transformations for differential equations involving arbitrary functions

A new efficient method for finding generalized equivalence transformations for a class of differential equation systems via its related extended classical symmetries is presented. This technique can be further adapted to find the equivalence transformations for the mathematical model. It applies to classes of differential systems whose arbitrary functions involve all equations’ independent variables. As a consequence, any symbolic manipulation program designed to find classical Lie symmetries can also be used to determine generalized equivalence transformations and equivalence transformations, respectively, without any modification of the program. The method has been implemented as the maple routine gendefget and is based on the maple package desolv(by Carminati and Vu). The nonlinear stationary heat conduction parameter identification problem is considered as an example.