A positive numerical scheme for a mixed-type partial differential equation model for fungal growth

Authors:
Graeme P. Boswell;Helen Jacobs;Fordyce A. Davidson;Geoffrey M. Gadd;Karl Ritz
Affiliations:
Department of Mathematics, University of Dundee, Dundee, DD1 4HN, UK;Division of Environmental and Applied Biology, Biological Sciences Institute, School of Life Sciences, University of Dundee, Dundee, DD1 4HN, UK;Department of Mathematics, University of Dundee, Dundee, DD1 4HN, UK;Division of Environmental and Applied Biology, Biological Sciences Institute, School of Life Sciences, University of Dundee, Dundee, DD1 4HN, UK;National Soil Resources Institute, Cranfield University, Silsoe, MK45 4DT, UK and Soil Plant Dynamics Unit, Scottish Crop Research Institute, Invergowrie, Dundee DD2 5DA, UK
Venue:
Applied Mathematics and Computation
Year:
2003

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Abstract

We describe a numerical scheme for the solution of a mixed-type PDE system which arises in the modelling of fungal growth. Given the application, conservation of mass and preservation of positivity are of paramount importance. The scheme employs a method of lines approach in which the system is split into hyperbolic and parabolic parts. Positivity and conservation of mass are ensured by the use of generalised flux functions and, in particular, flux limiters. The spatial discretisation results in stiff and non-stiff components which are solved using implicit and explicit methods respectively. Properties of the scheme are investigated via comparison with experimental data and performance is compared with another method of solution.