Among the numerical inverse Laplace transformation (NILT) methods, those that belong to Abate-Whitt framework (AWF) are considered be most efficient ones currently. It is a characteristic feature of AWF NILT procedures they independent transform function and time point interest. In this work we propose an procedure goes beyond limitation optimize accuracy utilizing also

It is known that the Laplace transform is frequently used to solve fractional-order differential equations. Unlike integer-order differential equations, fractional-order differential equations always lead to difficulties in calculating inversion of Laplace transforms. Motivated by finding an easy way to numerically solve the fractional-order differential equations, we investigated the validity ...

Based on recent results for 2-D continuous-discrete systems, this paper develops 2-D Laplace-z transform, which can be used to analyze 2-D continuous-discrete signals and system in Laplace-z hybrid domain. Current 1-D Laplace transformation and z transform can be combined into the new 2-D s-z transform. However, 2-D s-z transformation is not a simple extension of 1D transform, in 2-D case, we n...

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional deri...

The numerical inverse Laplace transformation NILM makes use of numerical integration. Generally, a high-order scheme of numerical integration renders high accuracy. However, surprisingly, this is not true for the NILM to the transfer function. Numerical examples show that the performance of higher-order schemes is no better than that of the trapezoidal scheme. In particular, the solutions from ...

Modified Laplace transformation method at finite temperature: application to infra-red problems of N component φ 4 theory ABSTRACT Modified Laplace transformation method is applied to N component φ 4 theory and the finite temperature problem in the massless limit is reexamined in the large N limit. We perform perturbation expansion of the dressed thermal mass in the massive case to several orde...

It is proposed a new approach for solution of the boundary problems for wide class of partial differential equations of mathematical physics, which includes the Laplace, Poisson and Helmholtz equations and parabolic equations. The approach is based on the discovered by author Local Ray Property and leads to new General Ray (GR) Method that uses the explicit analytical formulas with inverse Rado...

We investigate the effectiveness of Inverse Laplace Transform (ILT) analysis method to extract distribution relaxation rates from nuclear magnetic resonance data with stretched exponential relaxation. Stretched-relaxation is a hallmark rates, and an analytical expression exists for this case spin-1/2 nucleus. compare theoretical those extracted via ILT several values stretching exponent at diff...

A parallel numerical algorithm is introduced and analyzed for solving inhomogeneous initial-boundary value parabolic problems. The scheme is based on the method recently introduced in [8] for homogeneous problems. We give a method based on a suitable choice of multiple parameters. Our scheme allows to compute solutions in a wide range of time. Instead of using standard time-marching method, whi...