In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The ...

The time-dependent Schrödinger equation is discretized in space by a sparse grid pseudo-spectral method. The Strang splitting for the resulting evolutionary problem features first or second order convergence in time, depending on the smoothness of the potential and of the initial data. In contrast to the full grid case, where the frequency domain is the working place, the proof of the sufficien...

In this paper, we investigate the performance of pseudo-spectral methods in computing nearly singular solutions of fluid dynamics equations. We consider two different ways of removing the aliasing errors in a pseudo-spectral method. The first one is the traditional 2/3 dealiasing rule. The second one is a high (36th) order Fourier smoothing which keeps a significant portion of the Fourier modes...

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and tworing solutions. Combining our knowledge of the first four c...

It is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infiniteorder convergence (also called spectral accuracy) when they are smooth (e.g., [C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods for Fluid Dynamics, Springer-Verlag, Heidelberg, 1988; J.P. Boyd, Chebyshev and Fourier Spectral Methods, second ed., Dover, New...

Krylov subspace spectral (KSS) methods have been demonstrated to be effective tools for solving time-dependent variable-coefficient PDE. They employ techniques developed by Golub and Meurant for computing elements of functions of matrices to approximate each Fourier coefficient of the solution using a Gaussian quadrature rule that is tailored to that coefficient. In this paper, we apply this sa...

Block Krylov subspace spectral (KSS) methods are a “best-of-both-worlds” compromise between explicit and implicit time-stepping methods for variable-coefficient PDE, in that they combine the efficiency of explicit methods and the stability of implicit methods, while also achieving spectral accuracy in space and high-order accuracy in time. Block KSS methods compute each Fourier coefficient of t...

We have studied bounds on the neutrino mass using new data from the Sloan Digital Sky Survey measurement of the baryon acoustic peak. We find that even in models with a running spectral index where the number of neutrinos and the dark energy equation of state are allowed to vary, the bound on the sum of neutrino masses is robustly below 0.5 eV. Using the SDSS Lyman-α constraint on the amplitude...

Recent data, including the three–year WMAP data, the full 2dF galaxy power spectrum and the first–year data of the Supernova Legacy Survey, are used to constrain model parameters in quintessence cosmologies. In particular, we discuss the inverse power–law (RP) and SUGRA potentials and compare parameter constraints with those for ΛCDM. Both potentials fit current observations with a goodness of ...

In the present work, we introduce and explain a method of solution of the radiative transfer equation based on a thin cloud model. The efficiency of this method to retrieve dynamical chromospheric parameters from Stokes I profiles of Ca II 854.2 nm line showing spectral emission is investigated. The analyzed data were recorded with the Crisp Imaging Spectro-Polarimeter (CRISP) at Swedish 1-m So...