Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/89356
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dc.contributorDepartment of Applied Mathematicsen_US
dc.creatorLi, Ben_US
dc.creatorZhang, Jen_US
dc.creatorZheng, Cen_US
dc.date.accessioned2021-03-18T03:04:39Z-
dc.date.available2021-03-18T03:04:39Z-
dc.identifier.issn1064-8275en_US
dc.identifier.urihttp://hdl.handle.net/10397/89356-
dc.language.isoenen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2018, Society for Industrial and Applied Mathematics.en_US
dc.rightsPosted with permission of the publisher.en_US
dc.rightsThe following publication Li, B., Zhang, J., & Zheng, C. (2018). Stability and error analysis for a second-order fast approximation of the one-dimensional schrodinger equation under absorbing boundary conditions. SIAM Journal on Scientific Computing, 40(6), A4083-A4104 is available at https://dx.doi.org/10.1137/17M1162111en_US
dc.subjectAbsorbing boundary conditionen_US
dc.subjectError estimateen_US
dc.subjectFast algorithmen_US
dc.subjectGaussian quadratureen_US
dc.subjectSchrödinger equationen_US
dc.subjectStabilityen_US
dc.titleStability and error analysis for a second-order fast approximation of the one-dimensional schrödinger equation under absorbing boundary conditionsen_US
dc.typeJournal/Magazine Articleen_US
dc.identifier.spageA4083en_US
dc.identifier.epageA4104en_US
dc.identifier.volume40en_US
dc.identifier.issue6en_US
dc.identifier.doi10.1137/17M1162111en_US
dcterms.abstractA second-order Crank-Nicolson finite difference method, integrating a fast approximation of an exact discrete absorbing boundary condition, is proposed for solving the one-dimensional Schrödinger equation in the whole space. The fast approximation is based on Gaussian quadrature approximation of the convolution coefficients in the discrete absorbing boundary conditions. It approximates the time convolution in the discrete absorbing boundary conditions by a system of O(log 2 N) ordinary differential equations at each time step, where N denotes the total number of time steps. Stability and an error estimate are presented for the numerical solutions given by the proposed fast algorithm. Numerical experiments are provided, which agree with the theoretical results and show the performance of the proposed numerical method.en_US
dcterms.accessRightsopen accessen_US
dcterms.bibliographicCitationSIAM journal on scientific computing, 2018, v. 40, no. 6, p. A4083-A4104en_US
dcterms.isPartOfSIAM journal on scientific computingen_US
dcterms.issued2018-
dc.identifier.scopus2-s2.0-85060556004-
dc.identifier.eissn1095-7197en_US
dc.description.validate202103 bcvcen_US
dc.description.oaVersion of Recorden_US
dc.identifier.FolderNumbera0602-n04-
dc.identifier.SubFormID549-
dc.description.fundingSourceRGCen_US
dc.description.fundingText15300817en_US
dc.description.pubStatusPublisheden_US
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