The aim of this paper is to develop the mixed spectral and pseudospectral methods for nonlinear problems outside a disc, using Fourier and generalized Laguerre functions. As an example, we consider a nonlinear strongly damped wave equation. The mixed spectral and pseudospectral schemes are proposed. The convergence is proved. Numerical results demonstrate the efficiency of this approach. AMS su...

in this work, time domain analysis is used to solve adler’s equation in order to obtain the required time, for an oscillator under external injection, reaching the steady-state condition. mathematical approach has been applied to fully describe the transient of frequency acquisition in injection-locked lc and ring oscillators considering their time-varying nature. then, the analysis is verified...

The view of considering global Pseudospectral methods ~Sinc and Fourier! as the infinite order limit of local finite difference methods, and vice versa, finite difference as a certain sum acceleration of the pseudospectral methods is exploited to investigate high order finite difference algorithms for solving the Schrödinger equation in molecular dynamics. A Morse type potential for iodine mole...

In this paper, numerical solution of first-order systems of ordinary differential equations (ODEs) is considered and an error estimation method is proposed. By this method, the efficiency of pseudospectral method to solve the systems is determined and a modified pseudospectral method is presented. Furthermore, with providing some examples, the aforementioned cases are dealt with numerically. 20...

Abstract We exhibit a randomized algorithm which, given square matrix $$A\in \mathbb {C}^{n\times n}$$ A∈Cn×n with $$\Vert A\Vert \le 1$$ xmlns...

This paper explores the utility, tests the accuracy and examines the limitation of the discrete singular convolution (DSC) algorithm for solving partial differential equations (PDEs). The standard Fourier pseudospectral (FPS) method is also implemented for a detailed comparison so that the performance of the DSC algorithm can be better evaluated. Three twodimensional PDEs of different nature, t...

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The r...

We report what we believe to be the first simulation of enhanced backscattering (EBS) of light by numerically solving Maxwell's equations without heuristic approximations. Our simulation employs the pseudospectral time-domain (PSTD) technique, which we have previously shown enables essentially exact numerical solutions of Maxwell's equations for light scattering by millimeter-volume random medi...

Extreme-mass-ratio inspirals (EMRIs), stellar-mass compact objects (SCOs) inspiralling into a massive black hole, are one of the main sources of gravitational waves expected for the Laser Interferometer Space Antenna (LISA). To extract the EMRI signals from the expected LISA data stream, which will also contain the instrumental noise as well as other signals, we need very accurate theoretical t...