IJAM: Volume 38, No. 1 (2025)

DOI: 10.12732/ijam.v38i1.6

REVISITING FINITE DIFFERENCE

SOLUTIONS FOR HEAT-TYPE

EQUATIONS. PART II. ADVECTIVE TRANSFER

G. Garrido 1, J. L. G. Pestana 2

1 Departamento de Informatica

Universidad de Jaen

Campus Las Lagunillas, 23071 Jaen, SPAIN

2 Departamento de Fısica

Universidad de Jaen

Campus Las Lagunillas, 23071 Jaen, SPAIN

Abstract. In this second paper of a series, we revisit all major systematic uncertainties that affect a complete and unbiased sample of eleven finite

difference schemes for advection-like equations. In order to provide the coherent picture, unlike the existing way, we use as the key tenets both the

reverse Taylor’s analysis and the discrete Fourier’s analysis, as well as the monotonicity analysis. For every type of scheme, their theoretical

uncertainties are examined. A detailed graphical investigation is also provided and used to give a physical reinterpretation of the Courant-

Friedrichs-Lewy condition. We find that no scheme considered in this study resolves the smaller length scales well. Furthermore, we present

several numerical experiments on an equal footing corroborating our demonstrations and proving to what degree the accuracy of each scheme

is impaired by the discontinuities in the data. A comparison with each other is made as well. We definitively establish that the ingenious Lax-

Wendroff scheme is preferred by experiments.

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How to cite this paper?
DOI: 10.12732/ijam.v38i1.6
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 1

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