Numerische Mathematik

, Volume 49, Issue 5, pp 511–527

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

  • Guo Ben Yu
  • A. R. Mitchell
Asymptotic Behaviour and Acceleration of Iterative Sequences

DOI: 10.1007/BF01389703

Cite this article as:
Yu, G.B. & Mitchell, A.R. Numer. Math. (1986) 49: 511. doi:10.1007/BF01389703

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 

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Guo Ben Yu
    • 1
  • A. R. Mitchell
    • 2
  1. 1.Department of MathematicsShanghai University of Science and TechnologyShanghaiChina
  2. 2.Department of Mathematical SciencesUniversity of DundeeDundeeScotland, UK

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