In this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. This approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. The method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

hyperion hyperspectral data contains a very rich source of information from the earth surface that collects 242 narrow contiguous spectral bands. achieving this source of rich information is subject to the performance of suitable image processing methods on raw satellite data. satellite image processing methods can be classified into two categories of statistical-based and spectral-based. in th...

In this paper, we consider Chebyshev–Legendre Pseudo-Spectral (CLPS) method for solving coupled viscous Burgers (VB) equations. A leapfrog scheme is used in time direction, while CLPS method is used for space direction. Chebyshev–Gauss–Lobatto (CGL) nodes are used for practical computation. The error estimates of semi-discrete and fully-discrete of CLPS method for coupled VB equations are obtai...

‎‎In this article‎, ‎a new method is introduced to give approximate solution to Van der Pol equation‎. ‎The proposed method is based on the combination of two different methods‎, ‎the spectral Adomian decomposition method (SADM) and piecewise method‎, ‎called the piecewise Adomian decomposition method (PSADM)‎. ‎The numerical results obtained from the proposed method show that this method is an...

He, Ying Ph.D., Purdue University, December 2013. Efficient Spectral-Element Methods for Acoustic Scattering and Related Problems. Major Professor: Jie Shen . This dissertation focuses on the development of high-order numerical methods for acoustic and electromagnetic scattering problems, and nonlinear fluid-structure interaction problems. For the scattering problems, two cases are considered: ...

We consider the viscous Burgers equation with a fractional nonlinear term as a model involving non-local nonlinearities in conservation laws, which, surprisingly, has an analytical solution obtained by a fractional extension of the Hopf-Cole transformation. We use this model and its inviscid limit to develop stable spectral and discontinuous Galerkin spectral element methods by employing the co...

We present a graph spectral approach in which melodies are represented as graphs, based on the intervals between the notes they are composed of. These graphs are then indexed into a database using their laplacian spectra as a feature vector. This laplacian spectrum is a good representative of the original melody. Consequently, range searching around the query spectrum returns similar melodies.

In this paper, we investigate the spectral method on quadrilaterals. We introduce an orthogonal family of functions induced by Legendre polynomials, and establish some results on the corresponding orthogonal approximation. These results play important roles in the spectral method for partial differential equations defined on quadrilaterals. As examples of applications, we provide spectral schem...