Abstract
A numerical method is developed for a time dependent reaction diffusion two dimensional problem. This method is deduced by combining an alternating direction technique and the central finite difference scheme on some special piecewise uniform meshes. We prove that this method is uniformly convergent with respect to the diffusion parameter ε, achieving order 1 in both spatial and time variables. The theoretical results are confirmed by the numerical experiences performed.
This research has been partially supported by the CICYT project. num. AMB94-0396 and by a project of Gobierno de Navarra
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© 1997 Springer-Verlag Berlin Heidelberg
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Clavero, C., Jorge, J.C., Lisbona, F., Shishkin, G.I. (1997). Splitting time methods and one dimensional special meshes for reaction-diffusion parabolic problems. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_84
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DOI: https://doi.org/10.1007/3-540-62598-4_84
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