Spectral methods are a popular choice for constructing numerical approximations for smooth problems, as they can achieve geometric rates of convergence and have a relatively small memory footprint. In this paper, we introduce a general framework to convert a spectral-collocation method into a shootingbased variational integrator for Hamiltonian systems. We also compare the proposed spectral-col...

In this paper we propose, a collocation method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semiinfnite interval. This approach is based on generalized Laguerre polynomials and rational Chebyshev functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with...

When one approximates elliptic equations by the spectral collocation method on the Chebyshev-Gauss-Lobatto (CGL) grid, the resulting coefficient matrix is dense and illconditioned. It is known that a good preconditioner, in the sense that the preconditioned system becomes well conditioned, can be constructed with finite difference on the CGL grid. However, there is a lack of an efficient solver...

The unsteady heat, mass, and fluid transfer over a horizontal stretching sheet has been numerically investigated. Using a similarity transformation the governing time-dependent boundary layer equations for the momentum, heat, and mass transfer were reduced to a sets of ordinary differential equations. These set of ordinary differential equations were then solved using the Chebyshev pseudo-spect...

A highly accurate Fourier-Chebyshev spectral collocation method has been used to simulate flow in the wake of a sphere in the Reynolds number range from 350 to 650. Flow visualizations and frequency spectra provide a glimpse of the complex vortex dynamics that are observed in the sphere wake. It is found that in addition to the vortex shedding frequency which corresponds to the shedding of larg...

introduce a new class of numerical differentiation schemes constructed for the efficient solution of time-dependent PDEs that arise in wave phenomena. The schemes are constructed via the prolate spheroidal wave functions (PSWFs). Compared to existing differentiation schemes based on orthogonal polynomials, the new class of differentiation schemes requires fewer points per wavelength to achieve ...

We illustrate in the present paper how steady-state and unsteady-steady three-dimensional transport phenomena problems can be solved using the Chebyshev orthogonal collocation technique. All problems are elucidated using the ubiquitous software: MATLAB 1 . The treated case studies include: (1) unsteadystate heat conduction in a parallelepiped body, (2) quenching of a brick, (3) transient diffus...

A weighted orthogonal system on the half line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev ra...