Summary
A nonlinear partial difference equation resulting from discretising in space and time the parabolic reaction diffusion equation, which models the spruce budworm problem, is analysed and accuracy estimates obtained for solutions over afinite time range and ast→∞. Although the analysis is restricted to the logistic model in one space dimension, the techniques and comparison principles developed in the paper should prove useful in assessing the merits of numerical solutions of other nonlinear parabolic difference equations.
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During the period of this research Professor Guo Ben Yu was supported by a Science and Engineering Research Council visiting fellowship
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Yu, G.B., Mitchell, A.R. Analysis of a non-linear difference scheme in reaction-diffusion. Numer. Math. 49, 511–527 (1986). https://doi.org/10.1007/BF01389703
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DOI: https://doi.org/10.1007/BF01389703