Laplace transform inversion for late-time behavior of groundwater flow problems

Inversion of the Laplace transform

Let J% exp(-PQf(t) dt = F(P) P > 0 where b > 0 is a given number. We give a formula for f (t) in terms of F (p) , p > 0. The object of this Letter is to give a formula for the inverse Laplace transform in which the data used are given on the semi-axis p > 0 only. Let P>O where b > 0 is a fixed number. We have (1, formula 4.14.1) where Jo is a Bessel function. It follows from (1) and (2) that s,...

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 Methods for Laplace Transform Inversion

Laplace Transform Inversion and Passage-Time Distributions in Markov Processes

Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The formula for these inversions is expressed both as an explicit sum and in terms of a recurrence relation which is better suited to numerical computation. The recurrence for the inversion of certai...

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...