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Technical Issues
3/2016 pp. 141-146

Analiza dokładności obliczeniowej wybranych metod numerycznych wyznaczania odwrotnej transformaty Laplace’a

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This paper presents an analysis in terms of their accuracy of selected numerical methods for the inversion of the Laplace trans form. They were used to find solution of a gas flow model in real measuring system. The measurement unit, its application as well as its useful model were described in details in a work. We examined the Gaver-Stehfest method and the Honig and Hirdes method. The first one is based on combination of Gaver functionals. The second one is based on the Fourier series expansions. The results have confirmed the fact that the selected methods are suitable to solve analyzed problem, and showed that the algorithm developed by D. P. Gaver and H. Stehfest allows to obtain the best results of calculations. All calculations were using the computer algebra system Maple®. The presented algorithms have been implemented by the authors.

Key words

Laplace transform, numerical methods for the inversion of the Laplace transform, the Gaver-Stehfest method, the Honig and Hirdes, program Maple


1. Abate, J., Valkό, P., Multi-precision Laplace transform inversion, International Journal for Numerical Methods in Engineering, 2004, 60, pp. 979-993.

2. Cheng, A. H-D., Sidauruk, P., Approximate Inversion of the Laplace Transform, The Mathematical Journal, 1994, 4, pp. 76-82.

3. Chiang Li-Wei, The Application of Numerical Laplace Inversion Methods to Groundwater Flow and Solute Transport Problems, New Mexico Institute of Mining and Technology, 1989.

4. Davies, B., Martin, B., Numerical Inversion of the Laplace transform: a survey and comparison of methods, Journal of Computational Physics, 1978, 33, pp. 1-32.

5. Egonmwan, A.O., The Numerical Inversion of the Laplace Transform: Gaver-Stehfest, Piessens, and Regularized Collocation methods, LAP LAMBERT Academic Publishing: Saarbrücken, Germany, 2012.

6. Wang, Q., Zhan, H., 2015. On different numerical inverse Laplace methods for solute transport problems, Advances in Water Resources, 2015, 75, pp. 80-92. 

7. Wójcik, M., Szukiewicz, M., Kowalik, P., The application of the Laplace transform for modeling of gas flow using Maple®, The Journal of Applied Computer Science Methods, 2014, 6, pp. 43–53.

8. Zhang, J., Some innovative numerical approaches for pricing American options. University of Wollongong, Thesis Collection, 2007.