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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Volume were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on mdpi.com as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2004, 9(2), 183-189; doi:10.3390/mca9020183

A Formulation of Peaceman and Rachford ADI Method for the Three-Dimensional Heat Diffusion Equation

1
Dean of the Faculty of Computers & Informatics Zagazig University, Egypt
2
Faculty of Engineering, Shobra, Zagazig University, Banha branch, Egypt
3
Departrnent of Math. Faculty of Science Zagazig University, Egypt
*
Author to whom correspondence should be addressed.
Published: 1 August 2004
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Abstract

A formulation of an alternating direction implicit (ADI) method is given by extending peaceman and Rachford Scheme to three dimensions. The scheme becomes conditionally stable. The von Neumann stability analysis is performed. Numerical results for solving heat diffusion equation have been obtained for different specified boundary value problems to obtain a simple explicit stability.
Keywords: Heat-diffusion PDE; Boundary Value Problems; Von Neumann Stability Analysis; Numerical Methods; Finite Differences Heat-diffusion PDE; Boundary Value Problems; Von Neumann Stability Analysis; Numerical Methods; Finite Differences
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Ismail, I.A.; Zahran, E.H.; Shehata, M. A Formulation of Peaceman and Rachford ADI Method for the Three-Dimensional Heat Diffusion Equation. Math. Comput. Appl. 2004, 9, 183-189.

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