ASP: Automated symbolic computation of approximate symmetries of differential equations

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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. Program summaryProgram title: ASPCatalogue identifier: AEOG_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOG_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 15819No. of bytes in distributed program, including test data, etc.: 185052Distribution format: tar.gzProgramming language: MAPLE internal language.Computer: PCs and workstations.Operating system: Linux, Windows XP and Windows 7.RAM: Depends on the type of problem and the complexity of the system (small ≈ MB, large ≈ GB)Word size: Supports 32 and 64 bit platformsClassification: 4.3, 5.Nature of problem:Calculates approximate symmetries for differential equations using any of the three methods as proposed by Baikov, Gazizov and Ibragimov [1,2], Fushchych and Shtelen [3] or Pakdemirli, Yürüsoy and Dolapci [4]. Package includes an altered version of the DESOLVII package (Vu, Jefferson and Carminati [5]).Solution method:See Nature of problem above.Restrictions:Sufficient memory may be required for large systems.Running time:Depends on the type of problem and the complexity of the system (small ≈ seconds, large ≈ hours).