Abstract
In this paper some new linearly implicit methods are designed to solve evolutionary convection-diffusion problems with non linear reaction terms. Such methods combine the advantages of Alternating Direction Implicit methods and of Additive Runge-Kutta methods, which Cooper & Sayfy introduced (see [6], [7]) to solve non linear stiff problems with linearly implicit schemes. These new methods have an optimal order of computational complexity per time step and besides, under suitable smoothness requirements on the reaction terms, are unconditionally convergent. Some numerical experiences are shown confirming the expected efficiency and robustness of our methods.
This research is partially supported by the DGES PB97-1013, BFM2000-0803 and a project of University of La Rioja API-00/A24.
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Bujanda, B., Jorge, J.C. (2002). Numerical Methods for Evolutionary Convection-Diffusion Problems with Nonlinear Reaction Terms. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_93
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DOI: https://doi.org/10.1007/3-540-48086-2_93
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