Asymptotic Behaviour and Acceleration of Iterative Sequences

Numerische Mathematik

, Volume 49, Issue 5, pp 511-527

Analysis of a non-linear difference scheme in reaction-diffusion

  • Guo Ben YuAffiliated withDepartment of Mathematics, Shanghai University of Science and Technology
  • , A. R. MitchellAffiliated withDepartment of Mathematical Sciences, University of Dundee

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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.

Subject Classifications

AMS(MOS): 65MO5 CR: G1.8