In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multiorder fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is ve...

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 ...

This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebysh...

A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as a set of non-overlapping cubic regions, plus a set of maps to identify the faces of adjoining regions. The differential structure on these manifolds is fixe...

Pseudo-spectral method is one of the most accurate techniques for simulating turbulent flows. Fast Fourier transform (FFT) is an integral part of this method. In this paper, we present a new procedure to compute FFT in which we save operations during interprocess communications by avoiding transpose of the array. As a result, our transpose-free FFT is 15% to 20% faster than FFTW.

An orthogonal system of rational functions is introduced. Some results on rational approximations based on various orthogonal projections and interpolations are established. These results form the mathematical foundation of the related spectral method and pseudospectral method for solving differential equations on the half line. The error estimates of the rational spectral method and rational p...

In thermal plasma spectroscopy, Stark broadening measurement of hydrogen spectral lines is considered to be a good and reliable for electron density. Unlike intensity based measurements, measurements can pose problem interpretation when the light collected result spatial integration. Indeed, assuming no self-absorption emission lines, intensities simply add up but broadenings do not. order bett...

background: phic31 integrase system provides a new platform in various felid of research, mainly in gene therapy and creation of transgenic animals. this system enables integration of exogenous dna into preferred locations in mammalian genomes, which results in robust, long-term expression of the integrated transgene.objectives: identification of a novel pseudo attp site.materials and methods: ...

A fourth-order time-splitting Laguerre–Hermite pseudospectral method is introduced for Bose–Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The method is explicit, time reversible, and time transverse invariant. It conserves the position density and is spectral accurate in space and fourth-order accurate in time. Moreover, the new method has two other important advant...