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Search: authors:"Robert A. Van Gorder"

9 papers found.
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Dynamics from a predator-prey-quarry-resource-scavenger model

Allochthonous resources can be found in many foodwebs and can influence both the structure and stability of an ecosystem. In order to better understand the role of how allochthonous resources are transferred as quarry from one predator-prey system to another, we propose a predator-prey-quarry-resource-scavenger (PPQRS) model, which is an extension of an existing model for quarry...

Exact solution to a generalized model for compact stars

Recent work based on an approximation method suggested some odd behaviors may be possible in solutions to a generalized model for compact stars. We show that it was the error in these approximations and error coming from non-physical boundary conditions which lead to the odd behavior. As it turns out, the generalized model for compact stars actually admits an exact solution, and...

On the utility of the homotopy analysis method for non-analytic and global solutions to nonlinear differential equations

In recent work on the area of approximation methods for the solution of nonlinear differential equations, it has been suggested that the so-called generalized Taylor series approach is equivalent to the homotopy analysis method (HAM). In the present paper, we demonstrate that such a view is only valid in very special cases, and in general, the HAM is far more robust. In...

Two-Species Migration and Clustering in Two-Dimensional Domains

We extend two-species models of individual aggregation or clustering to two-dimensional spatial domains, allowing for more realistic movement of the populations compared with one spatial dimension. We assume that the domain is bounded and that there is no flux into or out of the domain. The motion of the species is along fitness gradients which allow the species to seek out a...

Reduction of dimension for nonlinear dynamical systems

We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for computing the solution when using a variety of analytical approaches. In the case where this reduction is possible, we employ differential elimination...

A Heat and Mass Transfer Model of a Silicon Pilot Furnace

. SLOMAN, COLIN P. PLEASE and ROBERT A. VAN GORDER are with the Mathematical Institute, University of Oxford , Oxford, OX2 6GG , UK. Contact The most common technological route for metallurgical silicon

Exact Stationary Solution Method for the Wadati-Konno-Ichikawa-Shimizu (WKIS) Equation

Robert A. Van Gorder 0 1 0 Subject Index: 010, 030 1 Department of Mathematics, University of Central Florida , Orlando, FL 32816-1364, USA We consider a method of obtaining exact implicit relations