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...

Radial basis function-Pseudospectral method and Fourier Pseudospectral (FPS) method are extended for stiff nonlinear partial differential equations with a particular emphasis on the comparison of the two methods. Fourth-order Runge-Kutta scheme is applied for temporal discretization. The numerical results indicate that RBF-PS method can be more accurate than standard Fourier pseudospectral meth...

A Fourier-matching pseudospectral modal method [PSMM(f)] is developed for analyzing lamellar diffraction gratings or grating stacks. A Chebyshev pseudospectral method is first used to accurately calculate the eigenmodes of the grating layers, and then the Fourier coefficients are matched at the interfaces between the layers. Compared with an existing pseudospectral modal method based on point m...

in the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. for this purpose, we replace the problem with an alternative optimal control problem in which the switching t...

In the paper, we derive a multi-symplectic Fourier pseudospectral method for Zhiber-Shabat equation. The Zhiber-Shabat equation, which describes many important physical phenomena, has been investigated widely in last several decades. The multi-symplectic geometry and multi-symplectic Fourier pseudospectral method for the Zhiber-Shabat equation is presented. The numerical experiments are given, ...

Acentral computational issue in solving infinite-horizonnonlinear optimal control problems is the treatment of the horizon. In this paper, we directly address this issue by a domain transformation technique that maps the infinite horizon to a finite horizon. The transformed finite horizon serves as the computational domain for an application of pseudospectral methods. Although any pseudospectra...

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System’s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transfor...