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.

scholarly journals Integral representations of Mittag-Leffler function on the positive real axis

2019 ◽  
Vol 20 (2) ◽  
pp. 217
Author(s):  
Eliana Contharteze Grigoletto ◽  
Edmundo Capelas Oliveira ◽  
Rubens Figueiredo Camargo
Keyword(s):  
Fractional Calculus ◽  
Laplace Transform ◽  
Real Axis ◽  
Integral Representations ◽  
Positive Real Axis ◽  
Inverse Laplace Transform ◽  
Positive Real

The Mittag-Leffler functions appear in many problems associated with fractional calculus. In this paper, we use the methodology for evaluation of the inverse Laplace transform, proposed by M. N. Berberan-Santos, to show that the three-parameter Mittag-Leffler function has similar integral representations on the positive real axis. Some of the integrals are also presented.

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

Numerical Inversion of Laplace Transform for Time Resolved Thermal Characterization Experiment

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
J. Toutain ◽  
J.-L. Battaglia ◽  
C. Pradere ◽  
J. Pailhes ◽  
A. Kusiak ◽  
...  
Keyword(s):  
Fourier Series ◽  
Laplace Transform ◽  
Periodic Function ◽  
Thermal Characterization ◽  
Inverse Laplace Transform ◽  
Numerical Inversion ◽  
Time Resolved ◽  
Reliable Technique ◽  
Numerical Inverse Laplace Transform ◽  
Thermal Disturbance

The aim of this technical brief is to test numerical inverse Laplace transform methods with application in the framework of the thermal characterization experiment. The objective is to find the most reliable technique in the case of a time resolved experiment based on a thermal disturbance in the form of a periodic function or a distribution. The reliability of methods based on the Fourier series methods is demonstrated.

Generalized coupled transient thermoelastic problem of multilayered spheres by the hybrid numerical method

2003 ◽  
Vol 217 (12) ◽  
pp. 1315-1323
Author(s):  
Z Y Lee ◽  
C L Chang
Keyword(s):  
Laplace Transform ◽  
Finite Difference Methods ◽  
Generalized Thermoelasticity ◽  
Inverse Laplace Transform ◽  
Hybrid Numerical Method ◽  
The Matrix ◽  
The Laplace Transform ◽  
Computational Procedures ◽  
Thermoelastic Problems ◽  
Matrix Similarity

This paper deals with axisymmetric quasi-static coupled thermoelastic problems for multilayered spheres. Laplace transforms and finite difference methods are used to analyse the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. Solutions are obtained for the temperature and thermal deformation distributions for the transient and steady state. It is demonstrated that the computational procedures established in this paper are capable of solving the generalized thermoelasticity problem of multilayered spheres.

scholarly journals An Extension of the Almost Isolated Singularity of Finite Exponential Order

1964 ◽  
Vol 14 (2) ◽  
pp. 137-141
Author(s):  
R. Wilson
Keyword(s):  
Real Axis ◽  
Taylor Series ◽  
Positive Real Axis ◽  
Isolated Singularity ◽  
Positive Real ◽  
Small Disk ◽  
Exponential Order ◽  
Disk Centre ◽  
Image Position

Let f(z) be represented on its circle of convergence |z| = 1 by the Taylor seriesand suppose that its sole singularity on |z| = 1 is an almost isolated singularity at z = 1. In the neighbourhood of such a singularity f(z) is regular on a sufficiently small disk, centre z = 1, with the outward drawn radius along the positive real axis excised. If also in this neighbourhood |f(z)| e−(1/δ)ρ remains bounded for some finite ρ, where δ is the distance from the excised radius, then the singularity is said to be of finite exponential order.

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