Tang Shi-min, Qin Su-di, R. O. Weber. Numerical Solution of a Nonlinear Reaction-Diffusion Equation[J]. Applied Mathematics and Mechanics, 1991, 12(8): 703-709.
Citation: Tang Shi-min, Qin Su-di, R. O. Weber. Numerical Solution of a Nonlinear Reaction-Diffusion Equation[J]. Applied Mathematics and Mechanics, 1991, 12(8): 703-709.

Numerical Solution of a Nonlinear Reaction-Diffusion Equation

  • Received Date: 1990-08-20
  • Publish Date: 1991-08-15
  • A nonlinear reaction-diffusion equation is studied numerically by a Petrov-Galerkin finite element method, which has been proved to be 2nd-order accurate in time and 4th-order in space. The comparison between the exact and numerical solutions of progressive waves shows that this numerical scheme is quite accurate, stable andefflcient. It is also shown that any local disturbance will spread, have a full growth and finally form two progressive waves propagating in both directions. The shape and the speed of the long term progressive waves are determined by the system itself, and do not depend on the details of the initial values.
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  • [1]
    Fisher,R.A.,The wave of advance of advantageous genes,Ann.of Eugen,7(1936),355-369.
    [2]
    Canosa,J.,Diffusion in nonlinear multiplication media.J.Math.Phys.,10(1969),1862-1868.
    [3]
    Canosa.J.,On a nonlinear diffusion equation describing population,growth,IBM J.Res.Develop.,17(1973),307-313.
    [4]
    Kolmogoroff,A.,I.Petrovaky and N.Piscounoff.Study of the diffusion equation with growth of the quantity of matter and its application to biology problem,Bulletin de I'Université délatã Moscou.Séreinternationale,Section A,1(1937).
    [5]
    Ramos,J.I.,Numerical solution of reaction-diffusion equation,Int.J.Comp.Maths.18(1985).43-66. 141-162;289-310.
    [6]
    Griffiths,D.F.and A.R.Mitchell.Stable periodic bifurcations of an explicit discretization of a nonlinear partial differential equation in reaction diffusion,IMA J.of Numer.Analy.,8(1988) 435-454.
    [7]
    Sachdev,P.L.,Nonlinear Diffusive Waves,Cambridge University Press(1987).103-105.
    [8]
    Wang,X.Y.,Exact and explicit solitary wave solutions for the generalized Fisher equation,Physics Letter A,131,(1988),277-279.
    [9]
    Gazdag,J.and J.Canosa,Numerical solution of Fisher's equation,J.Appl.Probab.,11(1974),445-457.
    [10]
    Evans,D.J.and M.S.Sahimi,The alternating group explicit(AGE)iterative method to solve parabolic and hyperbolic partial differential equations,Ann.of Numerical Fluid Mechanics and Heat Transfer,2(1989),283-389.
    [11]
    Tang,S.and R.O.Weber,Numerical study of Fisher's equation by a Petrov-Galerkin finite element method,J.Austral.Math.Soc.,Ser.B.(in press)
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