Computational aspects on numerical inversion of the Laplace Transform applied to transport problem
Keywords:
Transformada de Laplace; Métodos Numéricos; Problema de Condução de Calor.Abstract
The use of numerical inversion approaches becomes necessary when the Laplace Transform cannot be inverted analytically by usual techniques. However, the numerical inverse Laplace transform is generally an ill posed problem, and there is no universal method which works well for all problems. In this study, we selected four commonly used numerical inverse Laplace transform methods to evaluate their performance in dealing with heat conduction problems. This work explored the use of four methods for the numerical inversion of Laplace transform, in order to evaluate its performance in solving transient one-dimensional heat conduction problems: the Stehfest, the Fixed-Talbot, the Fourier Series and the Zakian methods. We specifically investigated, in this process, each method's optimal free parameters and its efficiency in elementary functions treatment. In this process, the Talbot-Fixed method proved to be efficient for the inversion of both functions with oscillatory behavior and involving decreasing exponentials. Specifically, for the latter class of functions, the methods of Stehfest and Zakian provided satisfactory results. In the study of the heat conduction problem, the four methods presented good performance, and the Talbot-Fixo presented better results (less absolute error) when compared to the others.
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