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A nonstandard finite difference method is proposed for the discretisation of the semilinear FitzHugh-Nagumo reaction diffusion equation. The equation has been useful in describing, for example, population models, biological models, heat and mass transfer models, and many other applications. The proposed approach involves splitting the equation into the space independent and the time independent sub equation. Numerical simulations for the full equation are presented. [ABSTRACT FROM AUTHOR]

In this work we consider an operator splitting numerical scheme for advection dominated material flow equation as given by the advection-diffusion-reaction equation. A model for multiphase flow is used to motivate the model under investigation. Dynamically consistent and positivity preserving nonstandard finite difference schemes are used to handle the split subproblems. Numerical simulations are presented to test the convergence of the split scheme. [ABSTRACT FROM AUTHOR]

This work considers the numerical solution of the Kuramoto-Sivashinsky equation using the fractional time splitting method. We will investigate the numerical behavior of two categories of the traveling wave solutions documented in the literature (Hooper & Grimshaw (1998)), namely: the regular shocks and the oscillatory shocks. We will also illustrate the ability of the scheme to produce convergent chaotic solutions. [ABSTRACT FROM AUTHOR]