Many-particle time domain methods are rising alternatives to particle-in-cell (PIC) or frequency simulate the wave–beam interactions in traveling wave tubes (TWTs). We focus on two of those: our Hamiltonian discrete model DIMOHA is compared analytically against pseudospectral method RUBEUS. Although based completely different approaches—the Gel’fand transform for and telegraphist circuit RUBEUS...

Pseudospectral methods are investigated for singularly perturbed boundary value problems for ordinary diierential equations which possess boundary layers. It is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions. We introduce here a new eeective procedure, based on coordinate stretching and the Che...

The optimal trajectory planning problem for multiple trains under fixed block signaling systems and moving block signaling systems is considered. Two approaches are proposed to solve this optimal control problem for multiple trains: the greedy approach and the simultaneous approach. In each solution approach, the trajectory planning problem is transformed into a mixed integer linear programming...

A new diagnostic for measuring the ability of atmospheric models to reproduce realistic low-frequency variability is introduced in the context of Held and Suarez’s 1994 proposal for comparing the dynamics of different general circulation models. A simple procedure to compute , the e-folding time scale of the annular mode autocorrelation function, is presented. This quantity concisely quantifies...

The post-optimality analysis of a tetrahedral formation flying optimal control problem is considered. In particular, this four-spacecraft orbit insertion problem is transcribed to a nonlinear programming problem (NLP) using a direct method called the Gauss pseudospectral method. The Karush-Kuhn-Tucker (KKT) conditions for this NLP are then derived and are compared to the conditions obtained via...

Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The design of the algorithm is based on using the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities that are typical when solving practical optimal control problems. The concept of pseudospectral ...

This paper analyses a Chebyshev pseudospectral collocation semidiscrete (continuous in time) discretization of a variable coefficient parabolic problem. Optimal stability and convergence estimates are given. The analysis is based on an approximation property concerning the GaussLobatto-Chebyshev interpolation operator.

We compare the long-time error bounds and spatial resolution of finite difference methods with different discretizations for Dirac equation small electromagnetic potentials characterized by ??(0,1] a dimensionless parameter. begin simple widely used time domain (FDTD) methods, establish rigorous them, which are valid up to at O(1/?). In estimates, we pay particular attention how errors depend e...

In [E. Babolian, M.M. Hosseini, Reducing index, and pseudospectral methods for differential-algebraic equations, Appl. Math. Comput. 140 (2003) 77–90], numerical solution of linear differential-algebraic equations (DAEs) has been presented by pseudospectral method. In this paper, a new error estimation technique is proposed to pseudospectral method such that is well done for linear semi-explici...