LIE

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 70 articles , 1 standard article )

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  1. Paliathanasis, Andronikos; Leach, P.G.L.: Nonlinear ordinary differential equations: a discussion on symmetries and singularities (2016)
  2. Sinkala, Winter; Nkalashe, Tembinkosi F.: Lie symmetry analysis of a first-order feedback model of option pricing (2015)
  3. Bozhkov, Y.; Dimas, S.: Group classification of a generalization of the Heath equation (2014)
  4. Adem, Abdullahi Rashid; Khalique, Chaudry Masood: New exact solutions and conservation laws of a coupled Kadomtsev-Petviashvili system (2013)
  5. Sinkala, W.; Chaisi, M.: Using Lie symmetry analysis to solve a problem that models mass transfer from a horizontal flat plate (2012)
  6. Vu, K.T.; Jefferson, G.F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
  7. Bihlo, Alexander; Popovych, Roman O.: Point symmetry group of the barotropic vorticity equation (2011)
  8. Caister, N.C.; Govinder, K.S.; O’Hara, J.G.: Solving a nonlinear PDE that prices real options using utility based pricing methods (2011)
  9. Dos Santos Cardoso-Bihlo, Elsa; Bihlo, Alexander; Popovych, Roman O.: Enhanced preliminary group classification of a class of generalized diffusion equations (2011)
  10. Kraenkel, R.A.; Senthilvelan, M.: On the particular solutions of an integrable equation governing short waves in a long-wave model (2011)
  11. Kweyama, M.C.; Govinder, K.S.; Maharaj, S.D.: Noether and Lie symmetries for charged perfect fluids (2011)
  12. Pradeep, R.Gladwin; Chandrasekar, V.K.; Senthilvelan, M.; Lakshmanan, M.: Nonlocal symmetries of a class of scalar and coupled nonlinear ordinary differential equations of any order (2011)
  13. Rocha Filho, Tarcísio M.; Figueiredo, Annibal: [SADE] a Maple package for the symmetry analysis of differential equations (2011)
  14. Sinkala, W.: Two ways to solve, using Lie group analysis, the fundamental valuation equation in the double-square-root model of the term structure (2011)
  15. Sophocleous, C.; O’Hara, J.G.; Leach, P.G.L.: Symmetry analysis of a model of stochastic volatility with time-dependent parameters (2011)
  16. Bihlo, Alexander; Popovych, Roman O.: Symmetry justification of Lorenz’ maximum simplification (2010)
  17. Ivanova, N.M.; Popovych, R.O.; Sophocleous, C.: Group analysis of variable coefficient diffusion-convection equations. I: Enhanced group classification (2010)
  18. Momoniat, E.; Mahomed, F.M.: Symmetry reduction and numerical solution of a third-order ODE from thin film flow (2010)
  19. Bihlo, Alexander; Popovych, Roman O.: Symmetry analysis of barotropic potential vorticity equation (2009)
  20. Edelstein, R.M.; Govinder, K.S.: Conservation laws for the Black-Scholes equation (2009)

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