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On a new method for finding generalized equivalence transformations for differential equations involving arbitrary functions. (English) Zbl 1218.34003

The author proposes an alternative method for obtaining generalized equivalence transformations by using the determining equations of the extended classical symmetries associated with the studied system of differential equations. This method not only provides interesting connections among group transformations but is more effective due to the small amount of calculations involved. The proposed method has been implemented in Maple as the GENDEFGET routine and uses the package DESOLV [K.Carminati and K. Vu, J. Symb. Comput. 29, No. 1, 95–116 (2000; Zbl 0958.68546)]. This routine can be used for parameter identification problems. The nonlinear stationary heat conduction parameter identification problem is considered as an example.

MSC:

34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
34A55 Inverse problems involving ordinary differential equations
34C14 Symmetries, invariants of ordinary differential equations

Citations:

Zbl 0958.68546

Software:

SYMMGRP; Maple; DESOLV
PDFBibTeX XMLCite
Full Text: DOI

References:

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