@Article{NMTMA-12-681,
author = {Wescley T. B. de Sousa and Carlos F. T. Matt},
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 = {<p style="text-align: justify;">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).</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2018-0026},
url = {http://global-sci.org/intro/article_detail/nmtma/13126.html}
}