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    ×
  • The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, Volume 33, Issue 1
  • July 1991, pp. 27-38

Numerical study of Fisher's equation by a Petrov-Galerkin finite element method

  • S. Tang (a1) and R. O. Weber (a2)
  • DOI: http://dx.doi.org/10.1017/S0334270000008602
  • Published online: 01 February 2009
Abstract
Abstract

Fisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]J. Canosa , “Diffusion in nonlinear multiplicative media”, J. Math. Phys., 10 (1969) 1862–8.

[2]J. Canosa , “On a nonlinear diffusion equation describing population growth”, IBM J. Res. Develop, 17 (1973) 307–13.

[4]R. A. Fisher , “The wave of advance of advantageous genes”, Ann. of Eugen, 7 (1936) 355–69.

[5]J. Gazdag and J. Canosa , “Numerical solutions of Fisher's equation”, J. Appl. Prob., 11 (1974) 445–57.

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