Maximum error estimates for a compact difference scheme of the coupled nonlinear Schr?dinger–Boussinesq equations

Hu Xiuling; Wang Shanshan; Zhang Luming

摘要

Abstract > The coupled nonlinear Schr?dinger–Boussinesq (SBq) equations describe the nonlinear development of modulational instabilities associated with Langmuir field amplitude coupled to intense electromagnetic wave in dispersive media such as plasmas. In this paper, we present a conservative compact difference scheme for the coupled SBq equations and analyze the conservative property and the existence of the scheme. Then we prove that the scheme is convergent with convergence order type="mathematics"> O ( τ 2 ?+? h 4 ) in L <sub> ∞ </sub> ‐norm and is stable in L <sub> ∞ </sub> ‐norm. Numerical results verify the theoretical analysis. </abstract> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> > 耦合的非线性SCHR？Dinger-Boussinesq（SBQ）方程描述了与诸如等离子体之类的分散介质中的强烈电磁波相关联的调制稳定性的非线性发展。在本文中，我们为耦合的SBQ方程提供了一种保守的紧凑型差异方案，并分析了保守财产和该方案的存在。然后我们证明该方案是通过收敛令的收敛 type =“mathematics”> o </ i> （ τ</ i> 2 </ sup> ？+？ h </ i> 4 </ sup> 的） </ span> 在 l </ i> <sub> ∞</ i> </ sub> -norm并稳定 l </ i> <sub> ∞</ i> </ sub> -规范。数值结果验证了理论分析。 </ p> </摘要> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-26113/'>《Numerical Methods for Partial Differential Equations: An International Journal》</a> <b style="margin: 0 2px;">|</b><span>2019年第6期</span><b style="margin: 0 2px;">|</b><span>共29页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Hu Xiuling&option=202" target="_blank" rel="nofollow">Hu Xiuling;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Wang Shanshan&option=202" target="_blank" rel="nofollow">Wang Shanshan;</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Zhang Luming&option=202" target="_blank" rel="nofollow">Zhang Luming;</a> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> <p>School of Mathematics and StatisticsJiangsu Normal UniversityXuzhou China;</p> <p>College of ScienceNanjing University of Aeronautics and AstronauticsNanjing China;</p> <p>College of ScienceNanjing University of Aeronautics and AstronauticsNanjing China;</p> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/4646.html" title="数值分析">数值分析;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=compact difference scheme&option=203" rel="nofollow">compact difference scheme;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=maximum error estimates&option=203" rel="nofollow">maximum error estimates;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Schr?dinger–Boussinesq equations&option=203" rel="nofollow">Schr?dinger–Boussinesq equations;</a> </p> <div class="translation"> 机译：紧凑型差分方案;最大误差估计;SCHR？Dinger-Boussinesq方程; 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