LIE, a PC program for Lie analysis of differential equations. LIE is a self-contained PC program for the Lie analysis of ordinary or partial differential equations, either a single equation or a simultaneous set. It is written in the symbolic mathematics language MUMATH and will run on any PC. It comes as a complete program that incorporates the necessary parts of MUMATH and is ready to run. The previous version was for classical Lie analysis, finding the point symmetries of well-posed differential equations. This is now extended to contact, Lie-Backlund and nonclassical symmetries. Memory utilization has been improved and it can analyse the equations of magneto-hydrodynamics, a set of 9 partial differential equations in 12 variables.

References in zbMATH (referenced in 80 articles , 1 standard article )

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  1. Zhang, Lin; Han, Zhong; Chen, Yong: A direct algorithm Maple package of one-dimensional optimal system for group invariant solutions (2018)
  2. Kontogiorgis, Stavros; Sophocleous, Christodoulos: On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations (2017)
  3. Paliathanasis, Andronikos; Leach, P. G. L.: Nonlinear ordinary differential equations: a discussion on symmetries and singularities (2016)
  4. Okelola, M. O.; Govinder, K. S.; O’Hara, J. G.: Solving a partial differential equation associated with the pricing of power options with time-dependent parameters (2015)
  5. Sinkala, Winter; Nkalashe, Tembinkosi F.: Lie symmetry analysis of a first-order feedback model of option pricing (2015)
  6. Bozhkov, Y.; Dimas, S.: Group classification of a generalization of the Heath equation (2014)
  7. Bozhkov, Y.; Dimas, S.: Group classification of a generalized Black-Scholes-Merton equation (2014)
  8. Adem, Abdullahi Rashid; Khalique, Chaudry Masood: New exact solutions and conservation laws of a coupled Kadomtsev-Petviashvili system (2013)
  9. Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O.: Complete point symmetry group of the barotropic vorticity equation on a rotating sphere (2013)
  10. Govinder, K. S.: Symbolic implementation of preliminary group classiffication for ordinary differential equations (2013)
  11. O’Hara, J. G.; Sophocleous, C.; Leach, P. G. L.: Symmetry analysis of a model for the exercise of a barrier option (2013)
  12. Tehseen, Naghmana; Prince, Geoff: Integration of PDEs by differential geometric means (2013)
  13. Sinkala, W.; Chaisi, M.: Using Lie symmetry analysis to solve a problem that models mass transfer from a horizontal flat plate (2012)
  14. Vu, K. T.; Jefferson, G. F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
  15. Bihlo, Alexander; Popovych, Roman O.: Point symmetry group of the barotropic vorticity equation (2011)
  16. Caister, N. C.; Govinder, K. S.; O’Hara, J. G.: Optimal system of Lie group invariant solutions for the Asian option PDE (2011)
  17. Caister, N. C.; Govinder, K. S.; O’Hara, J. G.: Solving a nonlinear PDE that prices real options using utility based pricing methods (2011)
  18. Dos Santos Cardoso-Bihlo, Elsa; Bihlo, Alexander; Popovych, Roman O.: Enhanced preliminary group classification of a class of generalized diffusion equations (2011)
  19. Kraenkel, R. A.; Senthilvelan, M.: On the particular solutions of an integrable equation governing short waves in a long-wave model (2011)
  20. Kweyama, M. C.; Govinder, K. S.; Maharaj, S. D.: Noether and Lie symmetries for charged perfect fluids (2011)

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