{"title":"含五次项的非线性Schrödinger方程的四阶紧致差分格式的最大范数误差估计。","authors":"Hanqing Hu, Hanzhang Hu","doi":"10.1186/s13660-018-1775-y","DOIUrl":null,"url":null,"abstract":"<p><p>A compact finite difference (CFD) scheme is presented for the nonlinear Schrödinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order <math><mi>O</mi><mo>(</mo><msup><mi>τ</mi><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>4</mn></msup><mo>)</mo></math> are proved by using the energy method. A numerical experiment is presented to support our theoretical results.</p>","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":"2018 1","pages":"180"},"PeriodicalIF":1.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1775-y","citationCount":"3","resultStr":"{\"title\":\"Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term.\",\"authors\":\"Hanqing Hu, Hanzhang Hu\",\"doi\":\"10.1186/s13660-018-1775-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>A compact finite difference (CFD) scheme is presented for the nonlinear Schrödinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order <math><mi>O</mi><mo>(</mo><msup><mi>τ</mi><mn>2</mn></msup><mo>+</mo><msup><mi>h</mi><mn>4</mn></msup><mo>)</mo></math> are proved by using the energy method. A numerical experiment is presented to support our theoretical results.</p>\",\"PeriodicalId\":49163,\"journal\":{\"name\":\"Journal of Inequalities and Applications\",\"volume\":\"2018 1\",\"pages\":\"180\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/s13660-018-1775-y\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inequalities and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13660-018-1775-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2018/7/20 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-018-1775-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/7/20 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
Maximum norm error estimates of fourth-order compact difference scheme for the nonlinear Schrödinger equation involving a quintic term.
A compact finite difference (CFD) scheme is presented for the nonlinear Schrödinger equation involving a quintic term. The two discrete conservative laws are obtained. The unconditional stability and convergence in maximum norm with order are proved by using the energy method. A numerical experiment is presented to support our theoretical results.
期刊介绍：
The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.
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