An Unconditionally Stable Laguerre Based Finite Difference Method for Transient Diffusion and Convection-Diffusion Problems

An Unconditionally Stable Laguerre Based Finite Difference Method for Transient Diffusion and Convection-Diffusion Problems

Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 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).

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2018-0026

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 681–708

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    28

Keywords:    Finite difference scheme Laguerre polynomials numerical methods diffusion and convection-diffusion problems.

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