Numerical Methods for Evolutionary Convection-Diffusion Problems with Nonlinear Reaction Terms

Authors:
Blanca Bujanda;Juan Carlos Jorge
Affiliations:
-;-
Venue:
PPAM '01 Proceedings of the th International Conference on Parallel Processing and Applied Mathematics-Revised Papers
Year:
2001

Citing 1
Cited 2

Stability results for fractional step discretizations of time dependent coefficient evolutionary problems

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Numerical methods for evolutionary reaction-diffusion problems with nonlinear reaction terms

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Efficient linearly implicit methods for nonlinear multidimensional parabolic problems

Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)

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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.