International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2570

Full Length Research Paper

Symmetry reductions and computational dynamics of a nonlinear reaction-diffusion problem with variable thermal conductivity

O. D.  Makinde1 and R. J. Moitsheki2*
  1Institute for Advanced Research in Mathematical Modelling and Computations, Cape Peninsula University of Technology, P. O. Box 1906, Bellville 7535, South Africa. 2Center for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, WITS, 2050, Johannesburg, South Africa.
Email: [email protected]

  •  Accepted: 21 March 2011
  •  Published: 04 April 2011

Abstract

 

In this paper, the nonlinear model for the reaction-diffusion problem with variable thermal conductivity is investigated. It is assumed that the model source term is an arbitrary function of temperature. Classical symmetry is employed to analyze all forms of the source term for which the governing equation admits extra point symmetries. A number of symmetries are obtained and some reductions are performed. Using the fourth-order Runge-Kutta method with a shooting technique, numerical solution of a reduced boundary value problem is obtained. Pertinent results are displayed graphically and discussed quantitatively.

 

Key words: Symmetry reduction, reaction-diffusion equation, variable thermal conductivity, shooting technique.