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；构造第 1 页ABSTRACTAt present, compact difference schemes have gradually become a main research direction of the numerical method of differential equations, and the compact difference schemes with high precision and good characteristics have been constructed one after another and applied to the numerical solution of some specific problems, and good results have been achieved. This topic for compact difference scheme, the research direction of hope can through MATLAB software such as aided and previous study of compact difference scheme to help to construct a compact difference scheme difference scheme, and by solving the differential equation numerical solution of experiments to verify its compact difference scheme features such as stability, convergence and error, finally can more intuitive understanding of the compact format the precision of the finite difference method, etc.Key words：Finite difference; Difference scheme; Structure第 2 页目录摘 要...............................................................................................................................................................2ABSTRACT....................................................................................................................................................31 引言...............................................................................................................
