The dynamics of a mathematical model of a layer of single phytoplankton species growing over a pool of nutrients, proposed by [A.H. Taylor, J.R.W. Harris, J. Aiken, The interaction of physical and biological process in a model of the vertical distribution of phytoplankton under stratification,...

The Westervelt wave equation can be used to describe non-linear propagation of finite amplitude sound. If one assumes that the medium can be treated as a thermoviscous fluid, a loss mechanism can be incorporated, but such a loss mechanism is not adequate if the medium is dispersive. In order to...

We construct a nonstandard finite difference (NSFD) scheme for a Burgers type partial differential equation (PDE) for which the diffusion coefficient has a linear dependence on the dependent variable. After a study of this PDE's traveling-wave solutions, we examine the corresponding properties...

We examine and discuss the general problem of how “denominator functions” are to be calculated when using nonstandard finite difference (NSFD) methods for constructing discrete models of differential equations. Using the example of the Fisher PDE with linear advection, we show that the...

The shallow water equations (SWE), which describe the flow of a thin layer of fluid in two dimensions have been used by the atmospheric modelling community as a vehicle for testing promising numerical methods for solving atmospheric and oceanic problems. The SWE are important for the study of...

Acoustic pulse propagation requires the inclusion of attenuation and its causal companion, dispersion when propagation is through a non-ideal fluid medium. For acoustic propagation in a linear medium, Szabo [T.L. Szabo, J. Acoust. Soc. Am., 96 (1994) 491–500] introduced the concept of a...

In this paper a class of models on nonlinear rods, which includes spatial inhomogeneities, varying cross-sectional area and arbitrary memory functions, is considered. The wave splitting technique is applied to provide a formulation suitable for numerical computation of direct and inverse...