<?xml version="1.1" encoding="utf-8"?>
<article xsi:noNamespaceSchemaLocation="http://jats.nlm.nih.gov/publishing/1.1/xsd/JATS-journalpublishing1-mathml3.xsd" dtd-version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><front><journal-meta><journal-id journal-id-type="publisher-id">EDTR</journal-id><journal-title-group><journal-title>Educational Theory Observation</journal-title></journal-title-group><issn>2995-5017</issn><eissn>2995-5025</eissn><publisher><publisher-name>Art and Technology</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.61369/EDTR.11756</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title>薛定谔方程的虚拟元分析</title><url>https://artdesignp.com/journal/EDTR/2/9/10.61369/EDTR.11756</url><author>刘旺</author><pub-date pub-type="publication-year"><year>2024</year></pub-date><volume>2</volume><issue>9</issue><history><date date-type="pub"><published-time>2024-09-20</published-time></date></history><abstract>本文旨在研究基于虚拟元方法的非线性Schr&amp;ouml;dinger方程(NLSW)的数值求解,该方程包含波动算子.首先,利用误差分裂技术将时空误差分解为时间误差和空间误差.其次,使用截断函数方法处理非线性项.误差分裂技术和截断函数方法在时间上采用隐式Crank-Nicolson方法,在空间上采用新的隐式虚拟元方法.最终,我们得到了NLSW方程的L2误差估计。</abstract><keywords>虚拟元方法,误差分裂技术,截断函数方法,误差估计</keywords></article-meta></front><body/><back><ref-list><ref id="B1" content-type="article"><label>1</label><element-citation publication-type="journal"><p>[1] D.Mora, G.Rivera, R.Rodr&amp;iacute;guez: A Virtual Element Method for the Steklov EigenvalueProblem. Mathematical Models and Methods in Applied Sciences, 25(2015)1421-1445.[2] G.Vacca, L.Beir&amp;atilde;o da Veiga: Virtual Element Methods for Parabolic Problems on Polyg-onal Meshes. Numerical Methods for Partial Differential Equations, 31(2017)2110-2134.[3] Hu, Y.Chen, A conservative difference scheme for two-dimensional nonlinear Schr&amp;ouml;ding-er equation with wave operator, Number. Methods Partial Differ. Equ. 32(3)(2015)862-876.[4] Y.Yang, H.Li, X.Guo, A linearized energy-conservative scheme for two-dimensional no-nlinear Schr&amp;ouml;dinger equation with wave operator, Appl. Math. Comput. 404(2021)126-234.[5] Meng Li: Cut-Off Error Splitting Technique for Conservative Nonconforming VEM forN-Coupled Nonlinear Schr&amp;ouml;dinger-Boussinesq Equations Journal of Scientific Computing,(2022)93:86.</p><pub-id pub-id-type="doi"/></element-citation></ref></ref-list></back></article>
