A stair Laguerre pseudospectral method is proposed for numerical solutions of differential equations on the half line. Some approximation results are established. A stair Laguerre pseudospcetral scheme is constructed for a model problem. The convergence is proved. The numerical results show that this new method provides much more accurate numerical results than the standard Laguerre spectral me...

In this paper we review some group theoretic techniques applied to discretizations of PDEs. Inspired by the recent years active research in Lie groupand exponential time integrators for differential equations, we will in the first part of the article present algorithms for computing matrix exponentials based on Fourier transforms on finite groups. As an example, we consider spherically symmetri...

The elastic wave equation in spherical coordinates is solved on a spherical section by a Chebyshev spectral method. In the presented algorithm the singularities in the governing equations are avoided by centering the physical domain around the equator. The highly accurate pseudo-spectral (PS) derivative operators reduce the required grid size compared to nite-diierence (FD) algorithms. The non-...

Article history: Received 24 February 2010 Received in revised form 4 June 2010 Accepted 6 July 2010 Available online 16 July 2010

The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical harmonics, that allows for the evolution of only those scalar fields which correspond to the divergence-free degrees of freedom of the vector/tensor. The full v...

This paper presents the application of adaptive rational spectral methods to the linear stability analysis of nonlinear fourth-order problems. Our model equation is a phase-field model of infiltration, but the proposed discretization can be directly extended to similar equations arising in thin film flows. The sharpness and structure of the wetting front preclude the use of the standard Chebysh...

We consider the max-plus analogue of the eigenproblem for matrix pencils, A ⊗ x = λ⊗ B ⊗ x. We show that the spectrum of (A, B) (i.e., the set of possible values of λ), which is a finite union of intervals, can be computed in pseudopolynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introdu...

In this paper, we use the spectral collocation method based on Chebyshev polynomials for spatial derivatives and fourth order Runge-Kutta (RK) method for time integration to solve the generalized Zakharov equation (GZE). Firstly, theory of application of Chebyshev spectral collocation method on the GZE is presented. This method yields a system of ordinary differential equations (ODEs). Secondly...

In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper si...

Traditionally, finite differences and finite element methods have been by many regarded as the basic tools for obtaining numerical solutions in a variety of quantum mechanical problems emerging in atomic, nuclear and particle physics, astrophysics, quantum chemistry, etc. In recent years, however, an alternative technique based on the semi-spectral methods has focused considerable attention. Th...