Abstract
In this paper, we originate results with finite difference schemes to approximate the solution of the classical Fisher Kolmogorov Petrovsky Piscounov (KPP) equation from population dynamics. Fisher’s equation describes a balance between linear diffusion and nonlinear reaction. Numerical example illustrates the efficiency of the proposed schemes, also the Neumann stability analysis reveals that our schemes are indeed stable under certain choices of the model and numerical parameters. Numerical comparisons with analytical solution are also discussed. Numerical results show that Crank Nicolson and Richardson extrapolation are very efficient and reliably numerical schemes for solving one dimension fisher’s KPP equation.
Highlights
Fisher gives introduction to nonlinear evolution equation to inquisitive, the proliferation of an beneficial gene in a population dynamics [1]
These values has been taken at some typical grid point (TGP) as we presents in Table 1 and Table 2
The solution of the Fishers equation is successfully approximated by a various numerical finite difference schemes
Summary
Fisher gives introduction to nonlinear evolution equation to inquisitive, the proliferation of an beneficial gene in a population dynamics [1]. The reaction diffusion Equation (1) express a model equation for the evolution of a neutron population in a nuclear reactor [2] and appears in chemical engineering applications [2]. This equation accommodates the effects of linear diffusion along uxx and nonlinear local multiplication or reaction along u (1 − u ) [3] [4]. The numerical model is consistent if the truncation error, that is the discrepancy between the finite difference approximation and the continuous derivatives, tends to zero as the grid spacing get smaller and smaller. We can say that, difference between the exact solution and approximated solution must vanish as the grid spacing tends to zero
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