Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method

• Published in: Numerical methods for partial differential equations Vol. 26; no. 4; pp. 979 - 992
• Main Authors: Dehghan, Mehdi, Taleei, Ameneh
• Format: Journal Article
• Language: English
• Published: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.07.2010
• Subjects: Chebyshev-Gauss-Lobbato (CGL) quadrature points; Fourier pseudo-spectral time splitting (FPTS) method; Gross-Pitaveskii (GP) equation; nonlinear Schrödinger equation (NLS); pseudo-spectral method; soliton; time-space pseudo-spectral (TSPS) method
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/num.20468

In this article, a time‐space pseudo‐spectral method is proposed for the numerical solution of nonlinear Schrödinger equation. The employed method is based on Chebyshev‐Gauss‐Lobbato quadrature points. Using the pseudo‐spectral differentiation matrices the problem is reduced to a system of nonlinear algebraic equations. However, this method is basically a spectral method, but a subdomain‐in‐time algorithm is used which yields a smaller nonlinear system to study long‐time numerical behavior. Because the time‐space pseudo‐spectral method has spectral accuracy, we present numerical experiments which show high accuracy of this method for the variant nonlinear Schrödinger equations and also particular attention is paid to the conserved quantities as an indicator of the accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010