an:05763433
Zbl 1195.65137
Dehghan, Mehdi; Taleei, Ameneh
Numerical solution of nonlinear Schr??dinger equation by using time-space pseudo-spectral method
EN
Numer. Methods Partial Differ. Equations 26, No. 4, 979-992 (2010).
00263195
2010
j
65M70 35Q55
nonlinear Schr??dinger equation; pseudo-spectral method; soliton; time-space pseudo-spectral method; Chebyshev-Gauss-Lobbato quadrature points; Fourier pseudo-spectral time splitting method; Gross-Pitaveskii equation; numerical experiments
Summary: A time-space pseudo-spectral method is proposed for the numerical solution of nonlinear Schr??dinger 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 Schr??dinger equations and also particular attention is paid to the conserved quantities as an indicator of the accuracy.