Program BIGLIE for Lie Analysis of Differential Equations on IBM Type PCs. Assumptions: You know why you want to use program LIE that finds the Lie group, or rather the Lie algebra, of differential equations, ordinary or partial, single or simultaneous, and you can use the output of this program to find special similarity solutions, conserved quantities, reductions of order etc. For example, you have seen the books ”Applications of Lie Groups to Differential Equations” by P. J. Olver ( and the worked examples in Chapters 2 and 3 ) or ”Symmetries and Differential Equations” by G. W. Blumen and S. Kumei or the article ”Symmetries of Differential Equations: from Sophus Lie to Computer Algebra” by F. Schwarz, SIAM Review, vol 30, Sept 1988, pp450-481. Many of the examples in the DAT files are from these sources. Source code is included. There is now a companion program BIGLIE51 that can handle problems that are too big for LIE.
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References in zbMATH (referenced in 5 articles )
Showing results 1 to 5 of 5.
- Zhang, Lin; Han, Zhong; Chen, Yong: A direct algorithm Maple package of one-dimensional optimal system for group invariant solutions (2018)
- Vu, K. T.; Jefferson, G. F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
- Rocha Filho, Tarcísio M.; Figueiredo, Annibal: [SADE] a Maple package for the symmetry analysis of differential equations (2011)
- Vu, K. T.; Butcher, J.; Carminati, J.: Similarity solutions of partial differential equations using DESOLV (2007)
- Butcher, J.; Carminati, J.; Vu, K. T.: A comparative study of some computer algebra packages which determine the Lie point symmetries of differential equations (2003)