A method for the numerical inversion of Laplace transforms

Hönig, Gerald; Hirdes, U.

doi:10.1016/0377-0427(84)90075-x

Cited by 1,007 publications

(581 citation statements)

References 4 publications

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“…In order to invert the Laplace transform, we adopt a numerical inversion method based on a Fourier series expansion Honig [31]. Using this method, the inverse   f t of the Laplace transform   f s is approximated by…”

Section: T T U C U T C T T T T C T X C X C Tmentioning

confidence: 99%

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

Bassiouny¹,

Sabry²

2013

JAMP

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A new mathematical model of time fractional order heat equation and fractional order boundary condition have been constructed in the context of the generalized theory of thermo piezoelasticity. The governing equations have been applied to a semi infinite piezoelectric slab. The Laplace transform technique is used to remove the time-dependent terms in the governing differential equations and the boundary condition. The solution of the problem is first obtained in the Laplace transform domain. Furthermore, a complex inversion formula of the transform based on a Fourier expansion is used to get the numerical solutions of the field equations which are represented graphically.

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Section: T T U C U T C T T T T C T X C X C Tmentioning

confidence: 99%

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

Bassiouny¹,

Sabry²

2013

JAMP

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“…The method, which is based on a Fourier series expansion proposed by Honig and Hirdes (1984) and is developed in detail in some literature (Ezzat et al 1999;Sherief et al 2010), is adopted to invert the Laplace transform in Eqs. (43).…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

Fractional thermoelasticity applications for porous asphaltic materials

Ezzat

2016

Pet. Sci.

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A new mathematical model of poro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with fractional order. One-dimensional application for a poroelastic half-space saturated with fluid is considered. The surface of the halfspace is assumed to be traction-free, permeable, and subjected to heating. The Laplace transform technique is used to solve the problem. The inversion of the Laplace transform will be obtained numerically and the numerical values of the temperature, stresses, strains, and displacements will be illustrated graphically for the solid and the liquid.

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“…The parameter c is a positive free parameter that must be greater than the real part of all the singularities of f (s) . The optimal choice of c was obtained according to the criteria described in Honig and Hirdes [24].…”

Section: Numerical Inversion Of the Laplace Transformmentioning

confidence: 99%

Sandwich structure panel subjected to thermal loading using fractional order equation of motion and moving heat source

Bassiouny

Youssef

2018

Can. J. Phys.

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The present work studies the thermoelastic behaviour of a model for a layered thin plate called Sandwich structure subjected to a thermal shock wave in the light of the generalized thermoelasticity theory using fractional order equation of motion in the presence of a moving heat source. The governing equations are solved using Laplace transform. To obtain the different inverse field functions numerically, we used a complex inversion formula of Laplace transform based on Fourier expansion. The effect of different parameters; namely; the speed, the strength of the heat source, fractional order and time on the thermodynamical temperature, stress and on the strain distribution, are discussed and presented graphically. Comparison with previous work in the context of the theory of generalized thermoelasticity shows that the present model is more reliable than the previous. The present model removes the points of discontinuity present in the stress and temperature distribution in the previous model. In the present model we found that the middle layer have affected slight by some of these parameters. The other new results are discussed.

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A method for the numerical inversion of Laplace transforms

Cited by 1,007 publications

References 4 publications

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

Fractional Order Two Temperature Thermo-Elastic Behavior of Piezoelectric Materials

Fractional thermoelasticity applications for porous asphaltic materials

Sandwich structure panel subjected to thermal loading using fractional order equation of motion and moving heat source

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