The most important feature of numerical methods based on a spectral decomposition is the best convergence rate (even infinite for infinitely regular functions) with respect to all other methods used in dealing with the solution to most of the differential equations. However this is true under the mandatory condition that at each time step of the evolving numerical solution no discontinuity occu...

This work presents a comparison between four classical spectral analyses: Fourier, multitaper, maximum entropy and iterative regression. Six 256-sample artificial series were generated by superposition of sine functions, long trends (of time scale greater than series length) and noise (generated by pseudo-random function). A spectral analysis of an observational time series (sunspot number) was...

A study of the free vibration of Timoshenko beams and axisymmetric Mindlin plates is presented. The analysis is based on the Chebyshev pseudospectral method, which has been widely used in the solution of fluid mechanics problems. Clamped, simply supported, free and sliding boundary conditions of Timoshenko beams are treated, and numerical results are presented for different thickness-to-length ...

The problem of magnetohydrodynamic flow and heat transfer of a viscous, incompressible, and electrically conducting fluid past a semi-infinite unsteady stretching sheet is analyzed numerically. The problem was studied under the effects of Hall currents, variable viscosity, and variable thermal diffusivity. Using a similarity transformation, the governing fundamental equations are approximated b...

The problem of determining minimum-fuel maneuver sequences for a four-spacecraft formation is considered. The objective of this paper is to find fuel-optimal spacecraft trajectories that transfer four spacecraft from an initial parking orbit to a desired terminal reference orbit while satisfying a set of constraints on the formation at the terminal time. Trajectories involving both one and two ...

While the Chebyshev pseudospectral method provides a spectrally accurate method, integration of partial differential equations with spatial derivatives of order M requires time steps of approximately O(N−2M ) for stable explicit solvers. Theoretically, time steps may be increased to O(N−M ) with the use of a parameter, α-dependent mapped method introduced by Kosloff and Tal-Ezer [J. Comput. Phy...

The paper addresses quaternion-based energy and time optimal spacecraft reorientation in the presence of complex attitude constrained zones. Designing an optimal reorientation trajectory for a rigid body spacecraft is posed as a nonlinear optimal control problem. In this direction, attitude constrained zones are defined with respect to the onboard instrument under two categories, forbidden and ...