Title: Two-grid discretization schemes for nonlinear Schrodinger equations
Authors: Chien, C. -S.
Huang, H. -T.
Jeng, B. -W.
Li, Z. -C.
應用數學系
Department of Applied Mathematics
Keywords: Schrodinger equation;two-grid discretization schemes;continuation;Adini's elements
Issue Date: 1-May-2008
Abstract: We study efficient two-grid discretization schemes with two-loop continuation algorithms for computing wave functions of two-coupled nonlinear Schrodinger equations defined on the unit square and the unit disk. Both linear and quadratic approximations of the operator equations are exploited to derive the schemes. The centered difference approximations, the six-node triangular elements and the Adini elements are used to discretize the PDEs defined on the unit square. The proposed schemes also can compute stationary solutions of parameter-dependent reaction-diffusion systems. Our numerical results show that it is unnecessary to perform quadratic approximations. (c) 2007 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.cam.2007.03.017
http://hdl.handle.net/11536/9405
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.03.017
Journal: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume: 214
Issue: 2
Begin Page: 549
End Page: 571
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