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Article

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

by
I. A. Ismail
1,
E. H. Zahran
2 and
M. Shehata
3,*
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.
Math. Comput. Appl. 2004, 9(2), 183-189; https://doi.org/10.3390/mca9020183
Published: 1 August 2004
Versions Notes

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

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MDPI and ACS Style

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. https://doi.org/10.3390/mca9020183

AMA Style

Ismail IA, Zahran EH, Shehata M. A Formulation of Peaceman and Rachford ADI Method for the Three-Dimensional Heat Diffusion Equation. Mathematical and Computational Applications. 2004; 9(2):183-189. https://doi.org/10.3390/mca9020183

Chicago/Turabian Style

Ismail, I. A., E. H. Zahran, and M. Shehata. 2004. "A Formulation of Peaceman and Rachford ADI Method for the Three-Dimensional Heat Diffusion Equation" Mathematical and Computational Applications 9, no. 2: 183-189. https://doi.org/10.3390/mca9020183

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