TY - JOUR
T1 - An Unconditionally Stable Laguerre Based Finite Difference Method for Transient Diffusion and Convection-Diffusion Problems
AU - Wescley T. B. de Sousa & Carlos F. T. Matt
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 - <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>