We develop an algorithm for numerically inverting multi-dimensional transforms. Our algorithm applies to any number of continuous variables (Laplace transforms) and discrete variables (generating functions). We use the Fourier-series method; i.e., the inversion formula is the Fourier series of a periodic function constructed by aliasing. This amounts to an application of the Poisson summation f...

Abstract The present work considers a two-dimensional (2D) heat conduction problem in the semi-infinite domain based on classical Fourier model and other non-Fourier models, e.g., Maxwell–Cattaneo–Vernotte (MCV) equation, parabolic, hyperbolic, modified hyperbolic dual-phase-lag (DPL) equations. Using integral transform technique, Laplace, transforms, we provide solution of (Green’s function) L...

The fast Fourier transform (FFT) is often used to compute numerical approximations to continuous Fourier and Laplace transforms. However, a straightforward application of the FFT to these problems often requires a large FFT to be performed, even though most of the input data to this FFT may be zero and only a small fraction of the output data may be of interest. In this note, the \fractional Fo...

The stress-strain state of a layered composite cylindrical shell under local heating by the environment due to convective heat exchange has been studied. equation six-modal theory thermoelasticity and two-dimensional thermal conductivity inhomogeneous anisotropic shells are used for this purpose. solution nonstationary transfer problem quasi-static finite hinged orthogonally reinforced symmetri...

This article presents the dynamic behavior of a semi-infinite interfacial crack in piezoelectric bimaterials under impact loading. With help transform methods (the Laplace transforms and Fourier transforms), problem is studied with Wiener–Hopf technique. strict proof guarantees feasibility this approach. The stress intensity factor electric displacement propagation characteristics are expressed...

In the chemical potential Stokes-Einstein formulation, when acceleration of the molecule is accounted for, a law of diffusion a capite ad calcem concentration results. In cartesian one-dimensional heat conduction in semi-infinite coordinates, the governing equation for temperature or concentration was solved for by the method of Laplace transforms. The results are in terms of the modified Besse...