稳定性计算r=511和r=59_偏微分方程.doc

扬州大学数学科学学院偏微分方程数值解法实验报告班级姓名学号实验名称验证最简查分格式的稳定性实验目的：就r=5/11,5/9用显格式，作树值试验，观察误差的增长规律，并说明r=5/11时稳定，r=5/9时不稳定。实验所用软件：JCreator实验过程记录（含：源程序（带注释）及异常情况记录等）r=5/11时import java.text.DecimalFormat;import java.util.Arrays;import java.lang.ArrayIndexOutOfBoundsException;public class A public static void main(String args)throws ArrayIndexOutOfBoundsExceptiondouble a = new double711;for(int i = 0;i7;i+)for (int j = 0;j11;j+)a05 = 1.0;for(int h = 0;h6;h+)for(int k = 1;k10;k+)ah+1k=(5*ahk+1+ahk+5*ahk-1)/11;DecimalFormat df=new DecimalFormat(0.0000);double tmp=ahk;System.out.print(df.format(tmp)+ );System.out.println();r=5/9时import java.text.DecimalFormat;import java.util.Arrays;import java.lang.ArrayIndexOutOfBoundsException;public class A public static void main(String args)throws ArrayIndexOutOfBoundsExceptiondouble a = new double711;for(int i = 0;i7;i+)for (int j = 0;j11;j+)a05 = 1.0;for(int h = 0;h6;h+)for(int k = 1;k10;k+)ah+1k = (5*ahk+1+ahk+5*ahk-1)/9;DecimalFormat df=new DecimalFormat(0.0000);double tmp=ahk;System.out.print(df.format(tmp)+ );System.out.println();实验结果（实验的输入数据和输出结果）r=5/11时0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4545 0.0909 0.4545 0.0000 0.0000 0.0000 0.0000 0.0000 0.2066 0.0826 0.4215 0.0826 0.2066 0.0000 0.0000 0.0000 0.0939 0.0563 0.2930 0.1134 0.2930 0.0563 0.0939 0.0000 0.0427 0.0342 0.1810 0.1038 0.2767 0.1038 0.1810 0.0342 0.0427 0.0194 0.1048 0.0792 0.2175 0.1195 0.2175 0.0792 0.1048 0.0194r=5/9时0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.5556 0.1111 0.5556 0.0000 0.0000 0.0000 0.0000 0.0000 0.3086 0.1235 0.6296 0.1235 0.3086 0.0000 0.0000 0.0000 0.1715 0.1029 0.5350 0.2071 0.5350 0.1029 0.1715 0.0000 0.0953 0.0762 0.4039 0.2317 0.6174 0.2317 0.4039 0.0762 0.0953 0.0529 0.2858 0.2159 0.5932 0.3260 0.5932 0.2159 0.285