Abstract
In this paper we present a numerical method to approximate the solution of 1D parabolic singularly perturbed problems of reaction-diffusion type. The method combines the Crank-Nicolson scheme and the central finite difference scheme defined on nonuniform special meshes. We give a new proof of the asymptotic behavior of the semidiscrete problems resulting after the time discretization. Numerical results show in practice almost second order of uniform convergence of the discrete method.
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References
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Acknowledgements
This research was partially supported by the projects MTM 2009-07637-E, MEC/FEDER MTM 2010-16917 and the Diputación General de Aragón.
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Clavero, C., Gracia, J.L. (2011). Uniformly Convergent Finite Difference Schemes for Singularly Perturbed 1D Parabolic Reaction–Diffusion Problems. In: Clavero, C., Gracia, J., Lisbona, F. (eds) BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Methods. Lecture Notes in Computational Science and Engineering, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19665-2_9
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DOI: https://doi.org/10.1007/978-3-642-19665-2_9
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