Observations on error in the application of the forward-difference method to the bulk diffusion equation

The Forward-Difference Method was applied to the one-dimensional diffusion equation for a problem with constant surface and initial solute concentrations and diffusivity independent of concentration. Two interesting observations were made on the error between the exact analytic solution and the nume...

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Bibliographic Details
Published in:Solid state ionics 1996-03, Vol.84 (1), p.73-76
Main Authors: Chung, Yong-Chae, Wuensch, Bernhardt J.
Format: Article
Language:English
Subjects:
Condensed matter: structure, mechanical and thermal properties
Diffusion in solids
Exact sciences and technology
Finite difference method
Forward—Difference Method
One-dimensional diffusion equation: Behavior of error
Physics
Random walk analysis
Theory of diffusion and ionic conduction in solids
Transport properties of condensed matter (nonelectronic)
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Summary:The Forward-Difference Method was applied to the one-dimensional diffusion equation for a problem with constant surface and initial solute concentrations and diffusivity independent of concentration. Two interesting observations were made on the error between the exact analytic solution and the numerical, solution: (1) when x equals √2 Dt, the Forward-Difference Method becomes very accurate no matter what value of λ ( = DΔ t/Δ x 2) was used; (2) the maximum error, which occurs at ∼ 2.76√ Dt, increased linearly with λ.
ISSN:0167-2738
1872-7689
DOI:10.1016/S0167-2738(96)83008-6