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On a discrete‐time collocation method for the nonlinear Schrödinger equation with wave operator
Author(s) -
Vong SeakWeng,
Meng QingJiang,
Lei SiuLong
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21729
Subject(s) - mathematics , collocation (remote sensing) , operator (biology) , scheme (mathematics) , order (exchange) , orthogonal collocation , mathematical physics , convergence (economics) , collocation method , differential operator , mathematical analysis , differential equation , ordinary differential equation , computer science , biochemistry , chemistry , finance , repressor , machine learning , economic growth , transcription factor , economics , gene
Abstract We consider a discrete‐time orthogonal spline collocation scheme for solving Schrödinger equation with wave operator. The scheme is proposed recently by Wang et al. (J Comput Appl Math 235 (2011), 1993–2005) and is showed to have high‐order convergence rate when a parameter θ in the scheme is not less than \documentclass{article} \usepackage{amsmath,amsfonts, amssymb}\pagestyle{empty}\begin{document}$\frac{1}{4}$\end{document} . In this article, we show that the result can be extended to include \documentclass{article} \usepackage{amsmath,amsfonts, amssymb}\pagestyle{empty}\begin{document}$\theta\in(0,\frac{1}{4})$\end{document} under an assumption. Numerical example is given to justify the theoretical result. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013