Application of best rational function approximation for Laplace transform inversion

Best rational function approximation to Laplace transform inversion using a window function (*)

The best ra t ional f unc t i on a p p r o x i m a t i o n for Laplace t ransform inversion due to L o n g m a n is mod i f i ed by the i n t r o d u c t i o n o f an appropr ia te " w i n d o w " func t ion . This w i n d o w f u n c t i o n enables one to a p p r o x i m a t e the inverse t r ans fo rm f( t) by a linear c o m b i n a t i o n gn (t) o f n exponent ia l func t ions accura te ly...

A method to obtain the best uniform polynomial approximation for the family of rational function

In this article, by using Chebyshev’s polynomials and Chebyshev’s expansion, we obtain the best uniform polynomial approximation out of P2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. Using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

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