Picture of virus under microscope

Research under the microscope...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs.

Strathprints serves world leading Open Access research by the University of Strathclyde, including research by the Strathclyde Institute of Pharmacy and Biomedical Sciences (SIPBS), where research centres such as the Industrial Biotechnology Innovation Centre (IBioIC), the Cancer Research UK Formulation Unit, SeaBioTech and the Centre for Biophotonics are based.

Explore SIPBS research

On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution

Beckett, G. and Mackenzie, J.A. (2001) On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution. Journal of Computational and Applied Mathematics, 131 (1-2). pp. 381-405. ISSN 0377-0427

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

We examine the convergence properties of a finite difference approximation of a singularly perturbed reaction-diffusion boundary value problem using a nonuniform grid. The grid is based on the equidistribution of a positive monitor function that is a linear combination of a constant floor and a power of the second derivative of the solution. Analysis shows how the monitor function can be chosen to ensure that the accuracy of the numerical approximation is insensitive to the size of the singular perturbation parameter. The use of equidistribution principles appears in many practical grid adaption schemes and our analysis provides insight into the convergence behaviour on such grids. Numerical results are given that confirm the uniform convergence rates.