 Error estimates of exponential wave integrator Fourier pseudospectral methods for the nonlinear Schrödinger equationBingquan Ji and Luming Zhang Applied Mathematics and Computation, 2019, vol. 343, issue C, 100-113 Abstract: In this article, several exponential wave integrator Fourier pseudospectra methods are developed for solving the nonlinear Schrödinger equation in two dimensions. These numerical methods are based on the Fourier pseudospectral discretization for spatial derivative first and then utilizing four types of numerical integration formulas, including the Gautschi-type, trapezoidal, middle rectangle and Simpson rules, to approximate the time integral in phase space. The resulting numerical methods cover two explicit and an implicit schemes and can be implemented effectively thanks to the fast discrete Fourier transform. Additionally, the error estimates of two explicit schemes are established by virtue of the mathematical induction and standard energy method. Finally, extensive numerical results are reported to show the efficiency and accuracy of the proposed new methods and confirm our theoretical analysis. Keywords: Nonlinear Schrödinger equation; Exponential wave integrator; Pseudospectral method; Error estimates (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:343:y:2019:i:c:p:100-113 DOI: 10.1016/j.amc.2018.09.041 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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