scholarly journals Inversion of the Laplace Transform from the Real Axis Using an Adaptive Iterative Method

2009 ◽  
Vol 2009 ◽  
pp. 1-38 ◽  
Author(s):  
Sapto W. Indratno ◽  
Alexander G. Ramm
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Laplace Transform ◽  
Real Axis ◽  
Quadrature Formula ◽  
Compact Support ◽  
Unknown Function ◽  
Stopping Rule ◽  
The Real ◽  
The Laplace Transform

A new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function is continuous with (known) compact support. An adaptive iterative method and an adaptive stopping rule, which yield the convergence of the approximate solution to , are proposed in this paper.

Diffraction by a wave-guide of finite length

1952 ◽  
Vol 48 (1) ◽  
pp. 118-134 ◽  
Author(s):  
D. S. Jones
Keyword(s):  
Electromagnetic Wave ◽  
Approximate Solution ◽  
Laplace Transform ◽  
Integral Equations ◽  
Finite Length ◽  
Wave Guide ◽  
The Laplace Transform ◽  
The Difference

AbstractWhen the electric intensities on two parallel planes, of which the two perfectly conducting sides of a wave-guide of finite length and infinite width are portions, are taken as unknowns, the problem of the diffraction of a plane harmonic electromagnetic wave polarized parallel to the edges of the guide leads to two integral equations. By means of the Laplace transform these equations are converted into others suitable for solution by successive substitutions. The series thus obtained is too complex for practical purposes, and so an approximate solution is found for the case when the length of the guide is large compared with the wavelength. Finally, there is a brief discussion of the difference between the distant fields when l is large and when l is infinite.

An easy and computable approximation for Troesch’s problem by using the Laplace Transform-Homotopy Perturbation Method

2019 ◽  
Vol 29 ◽  
pp. 1-14
Author(s):  
U. Filobello-Nino ◽  
H. Vazquez-Leal ◽  
A. L. Herrera-May ◽  
V. M. Jimenez-Fernandez ◽  
J. Cervantes-Perez ◽  
...  
Keyword(s):  
Approximate Solution ◽  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Absolute Relative Error ◽  
Homotopy Perturbation ◽  
Average Absolute Relative Error ◽  
The Laplace Transform ◽  
Troesch’S Problem

This work introduces the Laplace Transform-Homotopy Perturbation Method (LT-HPM) in order to provide an approximate solution for Troesch’s problem. After comparing figures between exact and approximate solutions, as well as the average absolute relative error (AARE) of the approximate solutions of this research, with others reported in the literature, it can be said that the proposed solutions are accurate and handy. In conclusion, LT-HPM is a potentially useful tool.

scholarly journals On linear viscoelasticity within general fractional derivatives without singular kernel

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 335-342 ◽  
Author(s):  
Feng Gao ◽  
Xiao-Jun Yang ◽  
Syed Mohyud-Din
Keyword(s):  
Laplace Transform ◽  
Mathematical Models ◽  
Present Article ◽  
Linear Viscoelasticity ◽  
Fractional Derivatives ◽  
Singular Kernel ◽  
The Real ◽  
The Laplace Transform ◽  
Mechanical Models

The Riemann-Liouville and Caputo-Liouville fractional derivatives without singular kernel are proposed as mathematical tools to describe the mathematical models in line viscoelasticity in the present article. The fractional mechanical models containing the Maxwell and Kelvin-Voigt elements are graphically discussed with the Laplace transform. The results are accurate and efficient to reveal the complex behaviors of the real materials.

On the numerical inversion of the Laplace transform

1964 ◽  
Vol 54 (6A) ◽  
pp. 1779-1795
Author(s):  
I. M. Longman
Keyword(s):  
Numerical Calculation ◽  
Laplace Transform ◽  
Real Axis ◽  
Positive Real Axis ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Positive Real ◽  
The Laplace Transform

abstract Methods are demonstrated for the numerical calculation of the inverse Laplace transform g(t) of a function g(p) given on the positive real axis of the p-plane.

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