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Erratum published on 1 December 2011, see Math. Comput. Appl. 2011, 16(4), 979.

Open AccessArticle
Math. Comput. Appl. 2010, 15(3), 449-460; doi:10.3390/mca15030449

High-Order Finite Difference Schemes for Solving the Advection-Diffusion Equation

1
Department of Mathematics, Faculty of Art and Science, Pamukkale University, Denizli 20070, Turkey
2
Department of Civil Engineering, Faculty of Engineering, Pamukkale University, Denizli 20070, Turkey
3
Department of Mathematics, Faculty of Art and Science, Süleyman Demirel University, Isparta 32260, Turkey
*
Author to whom correspondence should be addressed.
Published: 1 December 2010
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Abstract

Up to tenth-order finite difference schemes are proposed in this paper to solve one-dimensional advection-diffusion equation. The schemes based on high-order differences are presented using Taylor series expansion. To obtain the solutions, up to tenth-order finite difference schemes in space and a fourth-order Runge-Kutta scheme in time have been combined. The methods are implemented to solve two problems having exact solutions. Numerical experiments have been conducted to demonstrate the efficiency and high-order accuracy of the current methods. The techniques are seen to be very accurate in solving the advection-diffusion equation for Pe ≤ 5 . The produced results are also seen to be more accurate than some available results given in the literature.
Keywords: Advection-Diffusion Equation; Contaminant Transport; High-order Finite Difference Schemes; Runge-Kutta Advection-Diffusion Equation; Contaminant Transport; High-order Finite Difference Schemes; Runge-Kutta
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Sari, M.; Gürarslan, G.; Zeytinoğlu, A. High-Order Finite Difference Schemes for Solving the Advection-Diffusion Equation. Math. Comput. Appl. 2010, 15, 449-460.

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