ASP: Automated symbolic computation of approximate symmetries of differential equations

Jefferson, G.F., and Carminati, J. (2013) ASP: Automated symbolic computation of approximate symmetries of differential equations. Computer Physics Communications, 184 (3). pp. 1045-1063.

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A recent paper (Pakdemirli et al. (2004) [12]) compared three methods of determining approximate symmetries of differential equations. Two of these methods are well known and involve either a perturbation of the classical Lie symmetry generator of the differential system (Baikov, Gazizov and Ibragimov (1988) [7], Ibragimov (1996) [6]) or a perturbation of the dependent variable/s and subsequent determination of the classical Lie point symmetries of the resulting coupled system (Fushchych and Shtelen (1989) [11]), both up to a specified order in the perturbation parameter. The third method, proposed by Pakdemirli, Yürüsoy and Dolapçi (2004) [12], simplifies the calculations required by Fushchych and Shtelen's method through the assignment of arbitrary functions to the non-linear components prior to computing symmetries. All three methods have been implemented in the new MAPLE package ASP (Automated Symmetry Package) which is an add-on to the MAPLE symmetry package DESOLVII (Vu, Jefferson and Carminati (2012) [25]). To our knowledge, this is the first computer package to automate all three methods of determining approximate symmetries for differential systems. Extensions to the theory have also been suggested for the third method and which generalise the first method to systems of differential equations. Finally, a number of approximate symmetries and corresponding solutions are compared with results in the literature.

Item ID: 77715
Item Type: Article (Research - C1)
ISSN: 1879-2944
Keywords: Classical and approximate symmetries, Symbolic computation
Copyright Information: © 2012 Elsevier B.V. All rights reserved.
Date Deposited: 21 Feb 2023 00:26
FoR Codes: 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490399 Numerical and computational mathematics not elsewhere classified @ 100%
SEO Codes: 28 EXPANDING KNOWLEDGE > 2801 Expanding knowledge > 280118 Expanding knowledge in the mathematical sciences @ 100%
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