In this paper we deal with the e/ects on stability of subtle di/erences in formulations of pseudospectral methods for solution of the acoustic wave equation. We suppose that spatial derivatives are approximated by Chebyshev pseudospectral discretizations. Through reformulation of the equations as 4rst order hyperbolic systems any appropriate ordinary di/erential equation solver can be used to i...

An efficient and accurate exponential wave integrator Fourier pseudospectral (EWI-FP) method is proposed and analyzed for solving the symmetric regularized-long-wave (SRLW) equation, which is used for modeling the weakly nonlinear ion acoustic and space-charge waves. The numerical method here is based on a Gautschi-type exponential wave integrator for temporal approximation and the Fourier pseu...

The optimization and control problem for 4D trajectories is a subject rarely addressed in literature. In the 4D navigation problem we define waypoints, for each mission, where the arrival time is specified in each of them. One way to design trajectories for achieving this kind of mission is to use the trajectory optimization concepts. To solve a trajectory optimization problem we can use the in...

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 ...

The pseudospectral method is a highly accurate numerical scheme suitable for turbulence simulations. We have developed an open-source code, \textsc{\textsf{Calliope}}, which adopts the P3DFFT library \citep{Pekurovsky2012} to perform fast Fourier transform with two-dimensional (pencil) decomposition of grids. \textsc{\textsf{Calliope}} can solve incompressible magnetohydrodynamics (MHD), isothe...

Generally speaking, seismoelectric modeling is a prospecting method based on seismic and electromagnetic waves, in which waves generated by a seismic source at the boundary of the two environments generate a relative fluid-solid motion formed as a result of antagonism between the elastic properties of the environment with the saturated fluid. This research has as its objective, a study of the e...

We present a stable algorithm for constructing derivative matrices with small norm for pseudospectral methods. In particular, we construct second derivative matrices that incorporate Dirichlet or Neumann boundary conditions on an interval and on the disk. By construction, the norm of these matrices grows at the optimal rate O(N) for N -by-N matrices, in contrast to standard pseudospectral const...

Epilepsy is a neurological disorder in which patients have recurrent seizures. Seizures occur in conjunction with abnormal electrical brain activity which can be recorded by the electroencephalogram (EEG). Often, this abnormal brain activity consists of high amplitude regular spike-wave oscillations as opposed to low amplitude irregular oscillations in the non-seizure state. Active brain stimul...

Bratu's problem, which is the nonlinear eigenvalue equation Au + 2 exp(u)= 0 with u = 0 on the walls of the unit square and 2 as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance of symmett:v: because of invariance under the C 4 rotation group and parity in both x and y, one can slash the size of the basis set by a...