Dimsym is a program primarily for the determination of symmetries of differential equations. It also can be used to compute symmetries of distributions of vector fields or differential forms on finite dimensional manifolds, symmetries of geometric objects (eg, isometries), and also to solve linear partial differential equations. To use its primary function the user specifies a system of ordinary and/or partial differential equations and the type of symmetry to be found (Lie point, Lie-Backlund or some user-provided ansatz). Dimsym then produces the corresponding determining equations (a system of linear partial differential equations for the generator of the generic symmetry). It proceeds to solve these equations, reporting any special conditions required to produce a solution. Finally, Dimsym gives the generators of the symmetry group (which may of course be infinite dimensional). The program allows the user to compute Lie brackets, vector derivatives and so on and it has an interface with the REDUCE package EXCALC so that all the machinery of calculus on manifolds can be utilised from within the program. Its use can be interactive or batch and there are extensive tracing options.

References in zbMATH (referenced in 74 articles )

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  1. Moitsheki, Raseelo J.; Ntsime, Basetsana P.: Potential symmetry reduction of a convection-dispersion equation with spatial dependent water velocity (2021)
  2. Paliathanasis, Andronikos; Leach, P. G. L.: Nonlinear ordinary differential equations: a discussion on symmetries and singularities (2016)
  3. Maharaj, A.; Leach, P. G. L.: Application of symmetry and singularity analyses to mathematical models of biological systems (2014)
  4. Mhlongo, M. D.; Moitsheki, R. J.: Some exact solutions of nonlinear fin problem for steady heat transfer in longitudinal fin with different profiles (2014)
  5. Potsane, M. M.; Moitsheki, R. J.: Classification of the group invariant solutions for contaminant transport in saturated soils under radial uniform water flows (2014)
  6. Adem, Abdullahi Rashid; Khalique, Chaudry Masood: New exact solutions and conservation laws of a coupled Kadomtsev-Petviashvili system (2013)
  7. O’Hara, J. G.; Sophocleous, C.; Leach, P. G. L.: Symmetry analysis of a model for the exercise of a barrier option (2013)
  8. Tehseen, Naghmana; Prince, Geoff: Integration of PDEs by differential geometric means (2013)
  9. Harley, C.; Moitsheki, R. J.: Numerical investigation of the temperature profile in a rectangular longitudinal fin (2012)
  10. Sinkala, W.; Chaisi, M.: Using Lie symmetry analysis to solve a problem that models mass transfer from a horizontal flat plate (2012)
  11. Vu, K. T.; Jefferson, G. F.; Carminati, J.: Finding higher symmetries of differential equations using the MAPLE package DESOLVII (2012)
  12. 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)
  13. Sinkala, W.; Leach, P. G. L.; O’Hara, J. G.: Embedding the Vasicek model into the Cox-Ingersoll-Ross model (2011)
  14. Harley, C.: Hopscotch method: The numerical solution of the Frank-Kamenetskii partial differential equation (2010)
  15. Hayat, T.; Moitsheki, R. J.; Abelman, S.: Stokes’ first problem for Sisko fluid over a porous wall (2010)
  16. Moitsheki, R. J.; Makinde, O. D.: Classical Lie point symmetry analysis of nonlinear diffusion equations describing thermal energy storage (2010)
  17. Momoniat, E.; Mahomed, F. M.: Symmetry reduction and numerical solution of a third-order ODE from thin film flow (2010)
  18. Moitsheki, R. J.; Makinde, O. D.: Symmetry reductions and solutions for pollutant diffusion in a cylindrical system (2009)
  19. Momoniat, E.: Symmetries, first integrals and phase planes of a third-order ordinary differential equation from thin film flow (2009)
  20. Momoniat, E.: A thermal explosion in a cylindrical vessel: a non-classical symmetry approach (2009)

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