reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...

By using the numerical inverse Laplace transform based on modified Prudnikov formula, we construct solution of a nonstationary problem heat conduction for thermally sensitive half space operating in contact with layer under conditions convective exchange medium constant temperature. The thermoelastic state this piecewise homogeneous structure is investigated case where temperature kept surface.

In this paper we propose a transform method to compute the prices and greeks of barrier options driven by a class of Lévy processes. We derive analytical expressions for the Laplace transforms in time of the prices and sensitivities of single barrier options in an exponential Lévy model with hyper-exponential jumps. Inversion of these single Laplace transform yields rapid, accurate results. The...

Starting with a general definition of the Laplace transform on arbitrary time scales, we specify the Laplace transform on isolated time scales, prove several properties of the Laplace transform in this case, and establish a formula for the inverse Laplace transform. The concept of convolution is considered in more detail by proving the convolution theorem and a discrete analogue of the classica...

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...