{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,17]],"date-time":"2024-08-17T15:12:05Z","timestamp":1723907525947},"reference-count":45,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2015,6,1]],"date-time":"2015-06-01T00:00:00Z","timestamp":1433116800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"funder":[{"name":"EPSCoR & LaSPACE"},{"name":"National Science Foundation (NSF EPS 1003897)"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2015,6]]},"DOI":"10.1016\/j.amc.2015.03.053","type":"journal-article","created":{"date-parts":[[2015,4,8]],"date-time":"2015-04-08T23:01:13Z","timestamp":1428534073000},"page":"269-287","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":11,"special_numbering":"C","title":["A new compact finite difference scheme for solving the complex Ginzburg\u2013Landau equation"],"prefix":"10.1016","volume":"260","author":[{"given":"Yun","family":"Yan","sequence":"first","affiliation":[]},{"suffix":"III","given":"Frederick Ira","family":"Moxley","sequence":"additional","affiliation":[]},{"given":"Weizhong","family":"Dai","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/j.amc.2015.03.053_bib0001","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/j.chaos.2004.09.015","article-title":"Wave packet propagating in an electrical transmission line","volume":"24","author":"Lin","year":"2005","journal-title":"Chaos Solitons Fractals"},{"key":"10.1016\/j.amc.2015.03.053_bib0002","doi-asserted-by":"crossref","first-page":"3254","DOI":"10.1088\/0022-3727\/40\/10\/035","article-title":"Modulated waves and chaotic-like behaviours in the discrete electrical transmission line","volume":"40","author":"Ndzana","year":"2007","journal-title":"J. Phys. D: Appl. Phys."},{"key":"10.1016\/j.amc.2015.03.053_bib0003","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1142\/S0217979209049619","article-title":"Propagation of solitary waves on lossy nonlinear transmission lines","volume":"1","author":"Kengne","year":"2009","journal-title":"Int. J. Modern Phys. B"},{"key":"10.1016\/j.amc.2015.03.053_bib0004","first-page":"80","article-title":"On the dissipative complex Ginzburg-Landau equation governing the propagation of solitary pulses in dissipative nonlinear transmission lines","volume":"47","author":"Kengne","year":"2009","journal-title":"Chin. J. Phys."},{"key":"10.1016\/j.amc.2015.03.053_bib0005","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1007\/s10762-009-9485-7","article-title":"2D Ginzburg-Landau system of complex modulation for coupled nonlinear transmission lines","volume":"30","author":"Kengne","year":"2009","journal-title":"J. Infrared Millimeter Waves"},{"key":"10.1016\/j.amc.2015.03.053_bib0006","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1017\/S0013091500006210","article-title":"Fronts, domain walls and pulses in a generalized Ginzburg-Landau equations","volume":"38","author":"Duan","year":"1995","journal-title":"Proc. Edinb. Math. Soc."},{"key":"10.1016\/j.amc.2015.03.053_bib0007","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1016\/j.matcom.2005.03.006","article-title":"Exploding solition and front solutions of the complex cubic-quintic Ginzburg-Landau equation","volume":"69","author":"Soto-Crespo","year":"2005","journal-title":"Math. Comput. Simul."},{"key":"10.1016\/j.amc.2015.03.053_bib0008","doi-asserted-by":"crossref","first-page":"036621","DOI":"10.1103\/PhysRevE.73.036621","article-title":"Dynamical models for dissipative localized waves of the complex Ginzburg-Landau equation","volume":"73","author":"Tsoy","year":"2006","journal-title":"Phys. Rev. E"},{"key":"10.1016\/j.amc.2015.03.053_bib0009","doi-asserted-by":"crossref","first-page":"043839","DOI":"10.1103\/PhysRevA.76.043839","article-title":"Two-dimensional discrete Ginzburg-Landau solitions","volume":"76","author":"Efremidis","year":"2007","journal-title":"Phys. Rev. A"},{"key":"10.1016\/j.amc.2015.03.053_bib0010","doi-asserted-by":"crossref","first-page":"023814","DOI":"10.1103\/PhysRevA.77.023814","article-title":"Dissipative solitons in normal-dispersion fiber lasers","volume":"77","author":"Renninger","year":"2008","journal-title":"Phys. Rev. A"},{"key":"10.1016\/j.amc.2015.03.053_bib0011","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1137\/1034003","article-title":"Analysis and approximation of the Ginzburg-Landau model of superconductivity","volume":"34","author":"Du","year":"1992","journal-title":"SIAM Rev."},{"key":"10.1016\/j.amc.2015.03.053_bib0012","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1007\/BF01388682","article-title":"Finite element approximation of a periodic Ginzburg-Landau model for type-II superconductors","volume":"64","author":"Du","year":"1993","journal-title":"Numer. Math."},{"key":"10.1016\/j.amc.2015.03.053_bib0013","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1090\/S0025-5718-98-00954-5","article-title":"Discrete gauge invariant approximations of time dependent Ginzburg-Landau model of superconductivity","volume":"67","author":"Du","year":"1998","journal-title":"Math. Comput."},{"key":"10.1016\/j.amc.2015.03.053_bib0014","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1137\/S0036142996302852","article-title":"Analysis and convergence of covolume approximation of the Ginzburg-Landau model of superconductivity","volume":"35","author":"Du","year":"1998","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.amc.2015.03.053_bib0015","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1006\/jcph.2002.7128","article-title":"Modeling and computation of random thermal fluctuations and material defects in the Ginzburg-Landau model for superconductivity","volume":"181","author":"Deang","year":"2002","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.amc.2015.03.053_bib0016","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1016\/j.jcp.2004.06.009","article-title":"Numerical simulations of the quantized vortices on a thin superconducting hollow sphere","volume":"201","author":"Du","year":"2004","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.amc.2015.03.053_bib0017","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1090\/S0025-5718-04-01719-3","article-title":"Approximations of a Ginzburg-Landau model for superconducting hollow spheres based on spherical centroidal voronoi tessellations","volume":"74","author":"Du","year":"2005","journal-title":"Math. Comput."},{"key":"10.1016\/j.amc.2015.03.053_bib0018","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1088\/0951-7715\/4\/2\/003","article-title":"Finite-dimensional models of the Ginzburg-Landau equation","volume":"4","author":"Doelman","year":"1991","journal-title":"Nonlinearity"},{"key":"10.1016\/j.amc.2015.03.053_bib0019","doi-asserted-by":"crossref","first-page":"R15645","DOI":"10.1103\/PhysRevB.54.R15645","article-title":"Simulating the time-dependent dx2\u2212y2 Ginzburg-Landau equations using the finite-element method","volume":"54","author":"Wang","year":"1996","journal-title":"Phys. Rev. B"},{"key":"10.1016\/j.amc.2015.03.053_bib0020","doi-asserted-by":"crossref","first-page":"1483","DOI":"10.1137\/S003614299528554X","article-title":"Attractors and inertial manifolds for finite-difference approximations of the complex Ginzburg-Landau equation","volume":"34","author":"Lord","year":"1997","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.amc.2015.03.053_bib0021","first-page":"292","article-title":"A nonstiff Euler discretization of the complex Ginzburg-Landau equation in one space dimension","volume":"34","author":"Takac","year":"1997","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.amc.2015.03.053_bib0022","doi-asserted-by":"crossref","first-page":"1961","DOI":"10.1137\/S0036142998349102","article-title":"Adaptive Galerkin methods with error control for a dynamical Ginzburg-Landau model in superconductivity","volume":"38","author":"Chen","year":"2001","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.amc.2015.03.053_bib0023","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1080\/1023619031000146896","article-title":"A finite-difference solution of the Ginzburg-Landau equation","volume":"9","author":"Willers","year":"2003","journal-title":"J. Differ. Eq. Appl."},{"key":"10.1016\/j.amc.2015.03.053_bib0024","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1017\/S0956792507007140","article-title":"Numerical simulation of vortex dynamics in Ginzburg-Landau-Schr\u00f6dinger equation","volume":"18","author":"Zhang","year":"2007","journal-title":"Eur. J. Appl. Math."},{"key":"10.1016\/j.amc.2015.03.053_bib0025","doi-asserted-by":"crossref","first-page":"2466","DOI":"10.1137\/070700711","article-title":"On the time splitting spectral method of the complex Ginzburg-Landau equation in large time and space scale","volume":"30","author":"Degond","year":"2008","journal-title":"SIAM J. Sci. Comput."},{"key":"10.1016\/j.amc.2015.03.053_bib0026","doi-asserted-by":"crossref","first-page":"1190","DOI":"10.1080\/01630563.2010.510974","article-title":"Long-time behavior of finite difference approximations for the two-dimensional complex Ginzburg-Landau equation","volume":"31","author":"Zhang","year":"2010","journal-title":"Numer. Funct. Anal. Optimization"},{"key":"10.1016\/j.amc.2015.03.053_bib0027","first-page":"698","article-title":"On the convergence of difference schemes for the Kuramoto-Tsuzuki equation and for systems of reaction\u00a0diffusion type","volume":"31","author":"Tsertsvadze","year":"1991","journal-title":"J. Comput. Math. Math. Phys."},{"key":"10.1016\/j.amc.2015.03.053_bib0028","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1016\/S0377-0427(98)00135-6","article-title":"On Tsertsvadze\u2019s difference scheme for the Kuramoto-Tsuzuki equation","volume":"98","author":"Sun","year":"1998","journal-title":"J. Comput. Appl. Math."},{"key":"10.1016\/j.amc.2015.03.053_bib0029","unstructured":"X. Hu, Numerical methods on compact difference schemes for 1D nonlinear Kuramoto-Tsuzuki equation, Numer. Methods Partial Differ. Eq., in press."},{"key":"10.1016\/j.amc.2015.03.053_bib0030","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/0021-9991(92)90324-R","article-title":"Compact finite difference schemes with spectral-like resolution","volume":"103","author":"Lele","year":"1992","journal-title":"J. Computat. Phys."},{"key":"10.1016\/j.amc.2015.03.053_bib0031","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1360\/012010-846","article-title":"Unconditional convergence of two conservative compact difference schemes for non-linear Schr\u00f6dinger in one dimension","volume":"41","author":"Wang","year":"2011","journal-title":"Sci. Sin. Math."},{"key":"10.1016\/j.amc.2015.03.053_bib0032","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1016\/j.jcp.2013.03.007","article-title":"Fourth-order compact and energy conservative difference schemes for the nonlinear Schr\u00f6dinger equation in two dimensions","volume":"243","author":"Wang","year":"2013","journal-title":"J. Comput. Phys."},{"key":"10.1016\/j.amc.2015.03.053_bib0033","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1007\/s10915-013-9757-1","article-title":"Optimal point-wise error estimate of a compact difference scheme for the coupled Gross-Pitaevskii equations in one dimension","volume":"59","author":"Wang","year":"2014","journal-title":"J. Sci. Comput."},{"key":"10.1016\/j.amc.2015.03.053_bib0034","doi-asserted-by":"crossref","first-page":"58","DOI":"10.4208\/jcm.1310-m4340","article-title":"Optimal point-wise error estimate of a compact difference scheme for the coupled nonlinear Schr\u00f6dinger equations","volume":"32","author":"Wang","year":"2014","journal-title":"J. Comput. Math."},{"key":"10.1016\/j.amc.2015.03.053_bib0035","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/j.jmaa.2013.10.038","article-title":"Optimal point-wise error estimate of a compact difference scheme for the Klein-Gordon-Schr\u00f6dinger equation","volume":"412","author":"Wang","year":"2014","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/j.amc.2015.03.053_bib0036","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1007\/BF01386038","article-title":"Alternating direction and semi-explicit difference methods for parabolic partial differential equations","volume":"3","author":"Lees","year":"1961","journal-title":"Numer. Math."},{"key":"10.1016\/j.amc.2015.03.053_bib0037","first-page":"327","article-title":"On discrete energy method (i)","volume":"4","author":"Guo","year":"1984","journal-title":"Chin. Univ. J. Numer. Math."},{"key":"10.1016\/j.amc.2015.03.053_bib0038","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1137\/0729011","article-title":"An unconditionally stable three-level explicit difference scheme for the Schr\u00f6dinger equation with a variable coefficient","volume":"29","author":"Dai","year":"1992","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.amc.2015.03.053_bib0039","series-title":"Nonlinear Waves in Integrable and Non-integrable Systems","author":"Yang","year":"2010"},{"key":"10.1016\/j.amc.2015.03.053_bib0040","doi-asserted-by":"crossref","first-page":"1150005","DOI":"10.1142\/S179396231150005X","article-title":"High accuracy arithmetic average type discretization for the solution of two-space dimensional nonlinear wave equations","volume":"3","author":"Mohanty","year":"2012","journal-title":"Int. J. Model. Simul. Sci. Comput."},{"key":"10.1016\/j.amc.2015.03.053_bib0041","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1137\/0103003","article-title":"The numerical solution of parabolic and elliptic differential equations","volume":"3","author":"Peaceman","year":"1955","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"10.1016\/j.amc.2015.03.053_bib0042","series-title":"Numerical Methods of Partial Differential Equations","author":"Sun","year":"2012"},{"key":"10.1016\/j.amc.2015.03.053_bib0043","series-title":"Application of Discrete Functional Analysis to the Finite Difference Methods","author":"Zhou","year":"1990"},{"key":"10.1016\/j.amc.2015.03.053_bib0044","series-title":"An Introduction to Numerical Analysis","author":"Atkinson","year":"1989"},{"key":"10.1016\/j.amc.2015.03.053_bib0045","series-title":"Numerical Solution of Partial Differential Equations","author":"Morton","year":"1994"}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300315003677?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300315003677?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,8,23]],"date-time":"2019-08-23T00:55:33Z","timestamp":1566521733000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300315003677"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6]]},"references-count":45,"alternative-id":["S0096300315003677"],"URL":"https:\/\/doi.org\/10.1016\/j.amc.2015.03.053","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2015,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A new compact finite difference scheme for solving the complex Ginzburg\u2013Landau equation","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.amc.2015.03.053","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2015 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}