Abstract
The central difference scheme for reaction-diffusion problems, when fitted Shishkin type meshes are used, gives uniformly convergent methods of almost second order. In this work, we construct HOC (High Order Compact) compact monotone finite difference schemes, defined on a priori Shishkin meshes, uniformly convergent with respect the diffusion parameter ∈, which have order three and four except for a logarithmic factor. We show some numerical experiments which support the theoretical results.
This research was supported by the project DGES-PB97-1013
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Gracia, J.L., Lisbona, F., Clavero, C. (2001). High Order ε-Uniform Methods for Singularly Perturbed Reaction-Diffusion Problems. In: Vulkov, L., Yalamov, P., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2000. Lecture Notes in Computer Science, vol 1988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45262-1_41
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DOI: https://doi.org/10.1007/3-540-45262-1_41
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