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Theoretical analysis of the Exponential Transversal Method of Lines for the diffusion equation

✍ Scribed by A. J. Salazar; M. Raydan; A. Campo

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 375 KB
Volume: 16
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(200001)16:1<30::aid-num3>3.0.co;2-v

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✦ Synopsis

A new approximate technique to solve the diffusion equation, called the Exponential Transversal Method of Lines (ETMOL), utilizes an exponential variation of the dependent variable to improve accuracy in the evaluation of the time derivative. Campo and Salazar have implemented this method in a wide range of heat/mass transfer applications and have obtained surprisingly good numerical results. In this article, we study the theoretical properties of ETMOL in depth. In particular, consistency, stability, and convergence are established within the framework of the heat/mass diffusion equation. In most practical applications, the new method presents a very reduced truncation error in time, and its different versions are proven to be unconditionally stable in the Fourier sense. Convergence of the approximate solutions have then been established. The theory is corroborated by several analytical/numerical experiments that pose different levels of complexity.

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