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Volume 12, Issue 3
An Unconditionally Stable Laguerre Based Finite Difference Method for Transient Diffusion and Convection-Diffusion Problems

Wescley T. B. de Sousa & Carlos F. T. Matt

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 681-708.

Published online: 2019-04

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  • Abstract

This paper describes an application of weighted Laguerre polynomial functions to produce an unconditionally stable and accurate finite-difference scheme for the numerical solution of transient diffusion and convection-diffusion problems. The unconditionally stability of Laguerre-FDM (L-FDM) is guaranteed by expanding the time dependency of the unknown potential as a series of orthogonal functions in the domain (0, ∞), avoiding thus any time integration scheme. The L-FDM is a marching-on-in-degree scheme instead of traditional marching-on-in-time methods. For the two heat-transfer problems, we demonstrated the accuracy, numerical stability and computational efficiency of the proposed L-FDM by comparing its results against closed-form analytical solutions and numerical results obtained from classical finite-difference schemes as, for instance, the Alternating Direction Implicit (ADI).

  • AMS Subject Headings

34B60, 65N06, 78M20, 33C45

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-12-681, author = {}, title = {An Unconditionally Stable Laguerre Based Finite Difference Method for Transient Diffusion and Convection-Diffusion Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {3}, pages = {681--708}, abstract = {

This paper describes an application of weighted Laguerre polynomial functions to produce an unconditionally stable and accurate finite-difference scheme for the numerical solution of transient diffusion and convection-diffusion problems. The unconditionally stability of Laguerre-FDM (L-FDM) is guaranteed by expanding the time dependency of the unknown potential as a series of orthogonal functions in the domain (0, ∞), avoiding thus any time integration scheme. The L-FDM is a marching-on-in-degree scheme instead of traditional marching-on-in-time methods. For the two heat-transfer problems, we demonstrated the accuracy, numerical stability and computational efficiency of the proposed L-FDM by comparing its results against closed-form analytical solutions and numerical results obtained from classical finite-difference schemes as, for instance, the Alternating Direction Implicit (ADI).

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0026}, url = {http://global-sci.org/intro/article_detail/nmtma/13126.html} }
TY - JOUR T1 - An Unconditionally Stable Laguerre Based Finite Difference Method for Transient Diffusion and Convection-Diffusion Problems JO - Numerical Mathematics: Theory, Methods and Applications VL - 3 SP - 681 EP - 708 PY - 2019 DA - 2019/04 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0026 UR - https://global-sci.org/intro/article_detail/nmtma/13126.html KW - Finite difference scheme, Laguerre polynomials, numerical methods, diffusion and convection-diffusion problems. AB -

This paper describes an application of weighted Laguerre polynomial functions to produce an unconditionally stable and accurate finite-difference scheme for the numerical solution of transient diffusion and convection-diffusion problems. The unconditionally stability of Laguerre-FDM (L-FDM) is guaranteed by expanding the time dependency of the unknown potential as a series of orthogonal functions in the domain (0, ∞), avoiding thus any time integration scheme. The L-FDM is a marching-on-in-degree scheme instead of traditional marching-on-in-time methods. For the two heat-transfer problems, we demonstrated the accuracy, numerical stability and computational efficiency of the proposed L-FDM by comparing its results against closed-form analytical solutions and numerical results obtained from classical finite-difference schemes as, for instance, the Alternating Direction Implicit (ADI).

Wescley T. B. de Sousa & Carlos F. T. Matt. (2019). An Unconditionally Stable Laguerre Based Finite Difference Method for Transient Diffusion and Convection-Diffusion Problems. Numerical Mathematics: Theory, Methods and Applications. 12 (3). 681-708. doi:10.4208/nmtma.OA-2018-0026
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