Abstract In order to numerically invert Laplace transforms to calculate probability density functions (pdf’s) and cumulative distribution functions (cdf’s) in queueing and related models, we need to be able to calculate the Laplace transform values. In many cases the desired Laplace transform values (e.g., of a waiting-time cdf) can be computed when the Laplace transform values of component pdf...

the present study is the first to analyze the dynamic response of a poroelastic beam subjected to a moving force. moreover, the influences of attached mass-spring systems and non-ideal supports (with local movements in the supporting points or base due to the presence of factors such as gaps, unbalanced masses, and friction or seismic excitations) on the responses were investigated. non-ideal s...

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...

The method of Laplace transforms is used to find the distribution function, mean, and variance of the number of renewals of a renewal process whose inter-arrival time distribution has a rational Laplace transform. Where the Laplace transform is not rational, we use the Padé approximation method. We apply our method to certain examples and the results are compared to those reported by other rese...

Although Elzaki transform is stronger than Sumudu and Laplace transforms to solve the ordinary differential equations withnon-constant coefficients, but this method does not lead to finding the answer of some differential equations. In this paper, a method is introduced to find that a differential equation by Elzaki transform can be ‎solved?‎

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,...

Topological properties of the spaces of analytic test functions and distributions are investigated in the framework of the general theory of nonarchimedean locally convex spaces. The Laplace transform, topological isomorphism, is introduced and applied to the differential equations of nonarchimedean mathematical physics (Klein-Gordon and Dirac propagators).

In continuum one-dimensional space, a coupled directed continuous time random walk model is proposed, where the random walker jumps toward one direction and the waiting time between jumps affects the subsequent jump. In the proposed model, the Laplace-Laplace transform of the probability density function P(x, t) of finding the walker at position x at time t is completely determined by the Lapla...