中图分类号:O241单位代码:10231学硕士学位论文两类特殊延迟微分方程数值解的振动性分析号:42120788硕士研究生：刘诗梦导师：高建芳副教授学科专业：答辩日期：授予学位单位：计算数学2015年6月哈尔滨师范大学CLCNumber:O241SchoolCode:10231No:42120788AThesisSubmittedfortheDegreeofMasterOscillationAnalysisofNumericalSolutionforTwoKindsofSpecialDelayDifferentialEquationsMasterPostgraduate:Supervisor:Speciality:DateofDefense:DegreeAwarded:ShimengLiuAssociateProfessorJianfangGaoComputationalMathematicsJune,2015HarbinNormalUniversity目录目录摘要............................................................................IAbstract......................................................................II第1章绪论..................................................................11.1课题的背景及发展概述..................................................11.2延迟微分方程数值解的振动性的研究现状...............................21.3本文主要研究内容.......................................................5第2章预备知识.............................................................72.1延迟微分方程的振动理论................................................72.2差分方程的振动理论....................................................92.3几个重要不等式.........................................................9第3章方程x′(t)−ax(t)−a2x([t+2])=0数值解的振动性分析.............113.1解析解的振动性........................................................113.2θ-方法.................................................................133.3数值振动性和非振动性.................................................133.4数值算例...............................................................173.5本章小结...............................................................19第4章方程x′(t)+px(t)+qx(t−τ)=0数值解的振动性分析................204.1显式欧拉法............................................................214.2隐式欧拉法............................................................234.3梯形方法...............................................................254.4θ-方法.................................................................274.5数值算例...............................................................314.6本章小结...............................................................34结论..........................................................................35参考文献......................................................................36攻读硕士学位期间所发表的学术论文..........................................40原创性声明、使用授权书......................................................41致谢...........................................................................42CONTENTSCONTENTSAbstractinChinese..........................................................IAbstract......................................................................IIChapter1Introduction....................................................11.11.21.3Thebackgroundanddevelopmentofthesubject.......................1Theresearchstatusoftheoscillationfordelaydifferentialequation.....2Mainresearchcontent..................................................5Chapter2Preliminaries....................................................72.12.22.3Oscillationtheoryofdelaydifferentialequations.......................7Oscillationtheoryofdifferenceequations...............................9Severali...