We consider the numerical solution of nonlinear, dissipative partial differential equations using a pseudospectral method and the methodology of approximate inertial manifolds. Coarse and fine grids are employed, with a nonlinear mapping to relate the solutions computed on these grids. The approach is illustrated by consideration of the Kuramoto-Sivashinsky equation subject to periodic solution...

In this article we study the solvability of some boundary value problems for inhomogenous biharmobic equations. As a boundary operator we consider the differentiation operator of fractional order in the Miller-Ross sense. This problem is a generalization of the well known Neumann problems.

We present a pseudospectral formulation of the multireference single and double excitation configuration interaction method. A formal scaling advantage is achieved and practical timings are presented. The accuracy of the pseudospectral approximation within this method is probed for a variety of test cases. The method is typically accurate to within 1 mhartree while being up to six times faster ...

A novel Karhunen–Lo eve (KL) least-squares model for the supersonic flow of an inviscid, calorically perfect ideal gas about an axisymmetric blunt body employing shock-fitting is developed; the KL least-squares model is used to accurately select an optimal configuration which minimizes drag. Accuracy and efficiency of the KL method is compared to a pseudospectral method employing global Lagrang...

Nonplanar trajectory optimization problem with advanced variable specific impulse magnetoplasma rocket (VASIMR) engine is studied. A newly developed method called Gauss Pseudospectral method is applied to the nonplanar trajectory optimization problem with VASIMR engine. Three representative trajectory optimization problems are solved. The first is an orbit raising problem from LEO to GEO; the s...

entropy flux F is related to U and to the flux f by F 9 5 U 9f 9. The (weak) solution of (1.1)–(1.4) is then unique. We use the Legendre spectral viscosity method to solve nonlinear conservation laws. This method essentially consists in adding a In this paper, we are interested in computing the entropic spectral viscosity to the equations for the high wavenumbers of solution of Eq. (1.1), i.e.,...

The problem of performance optimization of a maneuvering re-entry vehicle is studied. The objective is to determine an optimal steering law for a high lift-to-drag ratio vehicle. An optimization criteria is derived that attempts to maximize the control margin of the vehicle in order to account for unmodeled perturbations during actual flight. The optimization problem is formulated as an optimal...

Decoupled fractional Laplacian wave equation can describe the seismic wave propagation in attenuating media. Fourier pseudospectral implementations, which solve the equation in spatial frequency domain, are the only existing methods for solving the equation. For the earth media with curved boundaries, the pseudospectral methods could be less attractive to handle the irregular computational doma...