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Math. Comput. Appl. 2016, 21(3), 32; doi:10.3390/mca21030032

Exponentially Fitted Finite Difference Schemes for Reaction-Diffusion Equations

Faculty of Arts and Natural Sciences, Usak University, 1 Eylul Campus, Usak 64200, Turkey
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Academic Editor: Fazal M. Mahomed
Received: 7 April 2016 / Revised: 10 July 2016 / Accepted: 11 July 2016 / Published: 20 July 2016
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Abstract

The purpose of this work is to introduce a new kind of finite difference formulation inspired from Fourier analysis, for reaction-diffusion equations. Compared to classical schemes, the proposed scheme is much more accurate and has interesting stability properties. Convergence properties and stability of the scheme are discussed. Numerical examples are provided to show better performance of the method, compared with other existing methods in the literature. View Full-Text
Keywords: exponentially fitted methods for differential equations; nonstandard finite differences; reaction-diffusion equations exponentially fitted methods for differential equations; nonstandard finite differences; reaction-diffusion equations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Erdoğan, U.; Akarbulut, K.; Tan, N.Ö. Exponentially Fitted Finite Difference Schemes for Reaction-Diffusion Equations. Math. Comput. Appl. 2016, 21, 32.

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