题目：紧致差分格式的构造和验证摘要目前，紧致差分格式已逐渐成为差分方程的数值方法的主要方向。具有良好特性的高精度的紧差分格式相继构造出来并能够应用到一些特殊的问题的数值求解，显现出了良好的效果。本课题针对紧致差分格式这一研究方向，希望能够通过MATLAB等软件的辅助以及前人对紧致差分格式的研究帮助对紧致差分格式进行构造一种差分格式，并且通过解微分方程的数值解实验对紧致差分格式进行验证其稳定性、收敛性以及误差等特性，最终能够比较直观了解这类紧致格式差分方法的精度等。关键词:有限差分；差分格式；构造ABSTRACTAtpresent,compactdifferenceschemeshavegraduallybecomeamainresearchdirectionofthenumericalmethodofdifferentialequations,andthecompactdifferenceschemeswithhighprecisionandgoodcharacteristicshavebeenconstructedoneafteranotherandappliedtothenumericalsolutionofsomespecificproblems,andgoodresultshavebeenachieved.Thistopicforcompactdifferencescheme,theresearchdirectionofhopecanthroughMATLABsoftwaresuchasaidedandpreviousstudyofcompactdifferenceschemetohelptoconstructacompactdifferenceschemedifferencescheme,andbysolvingthedifferentialequationnumericalsolutionofexperimentstoverifyitscompactdifferenceschemefeaturessuchasstability,convergenceanderror,finallycanmoreintuitiveunderstandingofthecompactformattheprecisionofthefinitedifferencemethod,etc.Keywords：Finitedifference;Differencescheme;Structure目录摘要...............................................................................................................................................................2ABSTRACT....................................................................................................................................................31引言..............................................................................................................................................................51.1有限差分方法简介...........................................................................................................................51.2紧致差分法研究概况.......................................................................................................................51.2.1抛物线方程............................................................................................................................51.2.2椭圆型方程............................................................................................................................61.2.3双曲线方程....................................................................................................................................61.3本文研究内容...................................................................................................................................62常见差分格式..............................................................................................................................................72.1显式差分格式...................................................................................................................................72.1.1古典显式格式的推导............................................................................................................72.2隐式差分格式...................................................................................................................................82.2.1古典隐式格式的推导.................................................................................
