毕业设计（论文）毕业设计题目：刚性系统的隐式RK方法学院：数理学院专业名称：信息与计算科学学号：201241210127学生姓名：丁楠指导教师：汪玉霞2016年05月15日毕业设计（论文）摘要本文主要介绍单步隐式Runge–Kutta方法,简要的介绍了Gauss型隐式Runge–Kutta方法、Radau型隐式Runge–Kutta方法和Lobatto型隐式Runge–Kutta方法。并利用这些基本的隐式Runge–Kutta方法来对刚性方程组进行数值求解，并将隐式Runge–Kutta方法与显式经典Runge–Kutta方法求解的结果进行对比，说明两种数值解法的优缺点。关键词：刚性系统隐式Runge–Kutta方法单步方法Newton迭代法AbstractThispapermainlyintroducestheImplicitRunge-KuttaMethodsandasimpledescriptionofGaussimplicitRunge-Kuttamethod,RadauimplicitRunge-KuttamethodandLobattoimplicitRunge-Kuttamethod.ThesebasicImplicitRunge-Kuttamethodsareusedtosolvethestiffequations.TheseimplicitRunge-KuttamethodsiarecomparedwiththeclassicalexplicitRunge-Kuttamethod.Thispaperexplaintheadvantagesanddisadvantagesofthetwokindofnumericalmethods.Keywords:StiffsystemImplicitRunge-KuttamethodOnestepmethodNewtoniterativemethod毕业设计（论文）目录1.绪论...............................................................................................................................11.1刚性方程.............................................................................................................11.2隐式RK方法的研究意义...................................................................................21.3RK方法的研究现状...........................................................................................32.单步RK方法的收敛性和稳定性................................................................................52.1单步RK方法的收敛性.......................................................................................52.2单步RK方法的稳定性.......................................................................................63.三类隐式RK方法........................................................................................................83.1引言.....................................................................................................................83.2Gauss型隐式RK方法........................................................................................93.3Radau型隐式RK方法.....................................................................................103.4Lobatto型隐式RK方法...................................................................................114隐式RK方法的实现..................................................................................................134.1非线性系统的改进............................................................................................134.2简化的Newton迭代法.....................................................................................135数值实验与结果分析.................................................................................................15参考文献........................................................................................................................18附录................................................................................................................................21毕业设计（论文）毕业设计（论文）1.绪论1.1刚性方程对于一般的线性常系数系统y'=Ay+φ(t)A为m×m的矩阵，特征值为λi(i=1,2,⋯,m)。定义1[23]若一个系统满足（1）ℜλi<0,i=1,2,⋯,m（2）maxi|ℜλi|/mini|ℜλi|=R≫1其中...
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