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

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

10.4208/nmtma.OA-2018-0026

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

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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-indegree scheme instead of traditional marching-on-in-time methods. For the two heattransfer 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).

  • History

Published online: 2019-04

  • AMS Subject Headings

34B60, 65N06, 78M20, 33C45

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