[PDF][PDF] Some recent advances on spectral methods for unbounded domains

J Shen, LL Wang - Communications in computational physics, 2009 - spms.ntu.edu.sg
We present in this paper a unified framework for analyzing the spectral methods in
unbounded domains using mapped Jacobi, Laguerre and Hermite functions. A detailed …

Mathematical theory and numerical methods for Bose-Einstein condensation

W Bao, Y Cai - arxiv preprint arxiv:1212.5341, 2012 - arxiv.org
In this paper, we mainly review recent results on mathematical theory and numerical
methods for Bose-Einstein condensation (BEC), based on the Gross-Pitaevskii equation …

[LLIBRE][B] Spectral and high-order methods with applications

T Tang - 2006 - math.purdue.edu
This book expands lecture notes by the authors for a course on Introduction of Spectral
Methods taught in the past few years at Penn State University, Simon Fraser University, the …

An approximation algorithm for the solution of the nonlinear Lane–Emden type equations arising in astrophysics using Hermite functions collocation method

K Parand, M Dehghan, AR Rezaei… - Computer Physics …, 2010 - Elsevier
In this paper we propose a collocation method for solving some well-known classes of Lane–
Emden type equations which are nonlinear ordinary differential equations on the semi …

Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane–Emden type

K Parand, M Shahini, M Dehghan - Journal of Computational Physics, 2009 - Elsevier
Lane–Emden equation is a nonlinear singular equation in the astrophysics that corresponds
to the polytropic models. In this paper, a pseudospectral technique is proposed to solve the …

A fourth-order time-splitting Laguerre--Hermite pseudospectral method for Bose--Einstein condensates

W Bao, J Shen - SIAM Journal on Scientific Computing, 2005 - SIAM
A fourth-order time-splitting Laguerre--Hermite pseudospectral method is introduced for
Bose--Einstein condensates (BECs) in three dimensions with cylindrical symmetry. The …

Rational Legendre approximation for solving some physical problems on semi-infinite intervals

K Parand, M Razzaghi - Physica scripta, 2004 - iopscience.iop.org
A numerical technique for solving some physical problems on a semi-infinite interval is
presented. Two nonlinear examples are proposed. In the first example the Volterra's …

Rational Chebyshev tau method for solving higher-order ordinary differential equations

K Parand, M Razzaghi - International Journal of Computer …, 2004 - Taylor & Francis
An approximate method for solving higher-order ordinary differential equations is proposed.
The approach is based on a rational Chebyshev (RC) tau method. The operational matrices …

Some progress in spectral methods

BY Guo - Science China Mathematics, 2013 - Springer
In this paper, we review some results on the spectral methods. We first consider the Jacobi
spectral method and the generalized Jacobi spectral method for various problems, including …

Sinc-collocation method for solving astrophysics equations

K Parand, A Pirkhedri - New Astronomy, 2010 - Elsevier
In this paper we propose Sinc-Collocation method for solving Lane–Emden equation which
is a nonlinear ordinary differential equation on a semi-infinite interval. It is found that Sinc …