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 82 articles , 1 standard article )

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  1. Rukanda, G. S.; Govinder, K. S.; O’Hara, J. G.: Option pricing: the reduced-form SDE model (2022)
  2. Zhang, Lin; Han, Zhong; Chen, Yong: A direct algorithm Maple package of one-dimensional optimal system for group invariant solutions (2018)
  3. Kontogiorgis, Stavros; Sophocleous, Christodoulos: On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations (2017)
  4. Paliathanasis, Andronikos; Leach, P. G. L.: Nonlinear ordinary differential equations: a discussion on symmetries and singularities (2016)
  5. 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)
  6. Sinkala, Winter; Nkalashe, Tembinkosi F.: Lie symmetry analysis of a first-order feedback model of option pricing (2015)
  7. Bozhkov, Y.; Dimas, S.: Group classification of a generalization of the Heath equation (2014)
  8. Bozhkov, Y.; Dimas, S.: Group classification of a generalized Black-Scholes-Merton equation (2014)
  9. Maharaj, A.; Leach, P. G. L.: Application of symmetry and singularity analyses to mathematical models of biological systems (2014)
  10. Adem, Abdullahi Rashid; Khalique, Chaudry Masood: New exact solutions and conservation laws of a coupled Kadomtsev-Petviashvili system (2013)
  11. Dos Santos Cardoso-Bihlo, Elsa; Popovych, Roman O.: Complete point symmetry group of the barotropic vorticity equation on a rotating sphere (2013)
  12. Govinder, K. S.: Symbolic implementation of preliminary group classiffication for ordinary differential equations (2013)
  13. O’Hara, J. G.; Sophocleous, C.; Leach, P. G. L.: Symmetry analysis of a model for the exercise of a barrier option (2013)
  14. Tehseen, Naghmana; Prince, Geoff: Integration of PDEs by differential geometric means (2013)
  15. Sinkala, W.; Chaisi, M.: Using Lie symmetry analysis to solve a problem that models mass transfer from a horizontal flat plate (2012)
  16. Vu, K. T.; Jefferson, G. F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
  17. Bihlo, Alexander; Popovych, Roman O.: Point symmetry group of the barotropic vorticity equation (2011)
  18. Caister, N. C.; Govinder, K. S.; O’Hara, J. G.: Optimal system of Lie group invariant solutions for the Asian option PDE (2011)
  19. Caister, N. C.; Govinder, K. S.; O’Hara, J. G.: Solving a nonlinear PDE that prices real options using utility based pricing methods (2011)
  20. Dos Santos Cardoso-Bihlo, Elsa; Bihlo, Alexander; Popovych, Roman O.: Enhanced preliminary group classification of a class of generalized diffusion equations (2011)

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