Numerical Methods for Laplace Transform Inversion

@inproceedings{Cohen2007NumericalMF,
  title={Numerical Methods for Laplace Transform Inversion},
  author={Alan M. Cohen},
  year={2007}
}
Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations. When solving such problems, in many cases it is fairly easy to obtain the Laplace transform, while it is very demanding to determine the inverse Laplace transform that is the solution of a given problem. Sometimes, after some difficult contour integration, we may find that a series solution results, but this may be quite difficult to evaluate in order to get an answer at… 
View via Publisher
link.springer.com
398 Citations
Highly Influential Citations
33
Background Citations
90
Methods Citations
117

398 Citations

Fully numerical Laplace transform methods

The role of the Laplace transform in scientific computing has been predominantly that of a semi-numerical tool. That is, typically only the inverse transform is computed numerically, with all steps…

Numerical Inverse Laplace Transform for Solving a Class of Fractional Differential Equations

The applications of numerical inversion of the Laplace transform method based on the Bernstein operational matrix to find the solution to a class of fractional differential equations are discussed and the advantages and computational implications are discussed.

Review of inverse Laplace transform algorithms for Laplace-space numerical approaches

Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time.

SOLVING SYSTEMS OF FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS VIA TWO DIMENSIONAL LAPLACE TRANSFORMS

The problem related to partial differential equation commonly can be solved by using a special integral transform, thus many authors solved the boundary value problems by using single Laplace…

Numerical Inversion of Laplace Transforms in the Solution of Transient Flow Problems With Discontinuities

Laplace transformation provides advantages in the solution of many pressure-transient analysis problems. Usually, these applications lead to a solution that needs to be inverted numerically to…

Performance comparison of numerical inversion methods for Laplace and Hankel integral transforms in engineering problems

Laplace inversion for the solution of an abstract heat equation without the forward transform of the source term

Compared to the existing contour quadratures, error analysis shows that the newquadrature possesses competitive asymptotic order of accuracy and numerical results show that when regularity of the initial term and/or differentiability of f(t) is not satisfied, the new quadrature is more accurate.

An algorithm for the inversion of Laplace transforms using Puiseux expansions

Tests show that the algorithm can be used to invert a wide range of Laplace transforms automatically with high accuracy and the output error estimator matches well with the true error.

An algorithm for the inversion of Laplace transforms using Puiseux expansions

This paper is devoted to designing a practical algorithm to invert the Laplace transform by assuming that the transform possesses the Puiseux expansion at infinity. First, the general asymptotic…

The Role of High Precision Arithmetic in Calculating Numerical Laplace and Inverse Laplace Transforms

In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the…
...