On the numerical inversion of Laplace transformations

Notes on Numerical Laplace Inversion

The main idea behind the Laplace transformation is that we can solve an equation (or system of equations) containing differential and integral terms by transforming the equation in time (t) domain into Laplace (2) domain. For example, we can use Laplace transforms to turn an initial value problem into an algebraic problem which is easier to solve. After we solved the problem in Laplace domain w...

Laplace transform numerical inversion v3.0

When running an analytical liquid rate simulation on a bounded reservoir an artefact due to Laplace transform numerical inversion algorithm can be noticed. This issue can be illustrated with a simple example: liquid rate simulation on a closed circular homogeneous reservoir with a fracture. The details of the simulation are graphically given in Figure 1(a). The simulation results can be seen in...

Numerical Inversion of the Laplace Transform

We give a short account on the methods for numerical inversion of the Laplace transform and also propose a new method. Our method is inspired and motivated from a problem of the evaluation of the Müntz polynomials (see [1]), as well as the construction of the generalized Gaussian quadrature rules for the Müntz systems (see [2]). As an illustration of our method we consider an example with 100 r...

Numerical Methods for Laplace Transform Inversion

Neutron Kinetics via Numerical Laplace Transform Inversion

A newly developed numerical Laplace transform inversion (NLTI) will be presented to determine the transient flux distribution within a subcritical fissile sample. The NLTI considered in this presentation has evolved to its present state over the past 10 years of application. The methodology adopted relies on the evaluation of the Bromwich contour through acceleration of the convergence of an in...