Numerische Mathematik

, Volume 111, Issue 2, pp 239–249 | Cite as

Robust convergence of a compact fourth-order finite difference scheme for reaction–diffusion problems

  • Torsten Linß


We consider a singularly perturbed one-dimensional reaction–diffusion problem with strong layers. The problem is discretized using a compact fourth order finite difference scheme. Altough the discretization is not inverse monotone we are able to establish its maximum-norm stability and to prove its pointwise convergence on a Shishkin mesh. The convergence is uniform with respect to the perturbation parameter. Numerical experiments complement our theoretical results.

Mathematics Subject Classification (2000)

65L10 65L12 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Institut für Numerische MathematikDresdenGermany

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