On different numerical inverse Laplace methods for solute transport problems

Wang, Quanrong; Zhan, Hongbin

doi:10.1016/j.advwatres.2014.11.001

Cited by 118 publications

(67 citation statements)

References 65 publications

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“…Finally the sum of finite integrals was calculated using the ɛseries acceleration algorithm of Wynn [38]. Wang and Zhan [36] thoroughly review the different inverse Laplace transform methods for solute transport problems.…”

Section: Numerical Inversion Of the Solutionmentioning

confidence: 99%

Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system

Sedghi

Samani

2015

Advances in Water Resources

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Section: Numerical Inversion Of the Solutionmentioning

confidence: 99%

Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system

Sedghi

Samani

2015

Advances in Water Resources

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“…Segundo [11], a versão original desse algoritmo [3] apresentava erros que foram corrigidos em [7]. A versão definitiva desse algoritmo é como segue:…”

Section: Algoritmo De Stehfestunclassified

Estudo comparativo de três algoritmos de inversão numérica da transformada de Laplace

Jesus

Costa

Fernández

et al. 2017

RBCA

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Resumo: Inúmeras aplicações na ciência e na tecnologia têm mostrado a utilidade da transformada de Laplace como ferramenta que auxilia na resolução dos modelos matemáticos correspondentes. Contudo, em diversas situações práticas, surge a necessidade de abordagens numéricas na inversão desta transformada por causa da dificuldade em se calcular analiticamente a integral de Bromwich que a define. No entanto, não existe nenhum método universal para a inversão numérica que funcione satisfatoriamente em todas as situações. Neste trabalho, apresenta-se um estudo comparativo do desempenho de três algoritmos de inversão numérica da transformada de Laplace, a saber, o algoritmo Talbot Abstract:Numerous applications in science and technology have shown the usefulness of the Laplace transform as a tool that assists in the resolution of the corresponding mathematical models. However, in several practical situations, the need for numerical approaches in the inversion of this transform arises because of the difficulty in analytically calculating the Bromwich integral that defines it. However, there is no universal method for numerical inversion that works satisfactorily in all situations. In this work, a comparative study of the performance of three numerical inversion algorithms of the Laplace transform, namely, the Abate and Valkó Fixed-Talbot algorithm, the Stehfest algorithm, and the Zakian algorithm, is presented.Keywords: Fixed-Talbot algorithm. Laplace transform. Numerical inversion. Stehfest algorithm. Zakian algorithm. IntroduçãoAs equações diferenciais descrevem o modo como certas grandezas variam com o tempo e/ou no espaço, tal como a corrente em um circuito elétrico, a oscilação de uma membrana vibrante ou ao fluxo de calor através de um condutor isolado. Essas equações geralmente estão associadas às condições iniciais que descrevem o estado do sistema no instante de tempo inicial ou de maneira mais geral, às condições de contorno [1]. Essas equações são aplicadas em diversas áreas da ciência, sendo extensamente utilizada em Engenharia elétrica e Engenharia química.Dentre as técnicas mais utilizadas na resolução de equações diferenciais encontra-se a transformada de Laplace, que é uma ferramenta operacional usualmente empregada na resolução de problemas de valor inicial que permite, por exemplo, transformar equações diferenciais ordinárias em equações algébricas.

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“…Fractional order differential equations are usually simpler to solve by applying the Laplace Transform than common methods of numerical integration [20][21][22][23]. However, the solutions in the Laplace space are often difficult to inverse, especially analytically.…”

Section: Introductionmentioning

confidence: 99%

Numerical calculations accuracy comparison of the Inverse Laplace Transform algorithms for solutions of fractional order differential equations

Brzeziński

Ostalczyk

2015

Nonlinear Dyn

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In the paper we present results of a numerical experiment in which we evaluate and compare some numerical algorithms of the Inverse Laplace Transform for inversion accuracy of some fractional order differential equations solutions. The algorithms represent diverse lines of approach to the subject of the numerical inversion and include methods by Stehfest, Abate and Whitt, Vlach and Singhai, De Hoog, Talbot, Zakian and a one in which the FFT is applied for Fourier series convergence acceleration. We used C++ and Python languages and applied arbitrary precision mathematical libraries to address some crucial issues of an numerical implementation. Introductory test set includes Laplace transforms which are considered as difficult to compute as well as some others commonly applied in fractional calculus. In the main part of the evaluation, there is assessed accuracy of the numerical Inverse Laplace Transform of some popular fractional differential equations solutions, e.g., the initial value problem in case of the inhomogeneous Bagley-Torvik equation and composite fractional oscillation equation. Evaluation results enable to conclude that the Talbot method which involves deformed Bromwich contour integration, the De Hoog and the Abate and Whitt meth-

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On different numerical inverse Laplace methods for solute transport problems

Cited by 118 publications

References 65 publications

Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system

Semi-analytical solutions for flow to a well in an unconfined-fractured aquifer system

Estudo comparativo de três algoritmos de inversão numérica da transformada de Laplace

Numerical calculations accuracy comparison of the Inverse Laplace Transform algorithms for solutions of fractional order differential equations

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