微分方程数值解欧拉法Word格式文档下载.docx

1、0.5712302.4053E-021.00.5290510.5518192.2768E-02当h=0.05时，解为：0.050.9500000.9524182.4185E-030.100.9048784.4835E-030.150.8641580.8703916.2326E-030.200.8274067.6996E-030.250.7942230.8031388.9155E-030.300.7642479.9084E-030.350.7371470.7478501.0704E-020.400.7126211.1324E-020.450.6903970.7021881.1791E-020.5

2、00.6702231.2124E-020.550.6518760.6642131.2338E-020.600.6351481.2450E-020.650.6198550.6323281.2473E-020.700.6058291.2420E-020.750.5929180.6052201.2302E-020.800.5809851.2129E-020.850.5699090.5818191.1909E-020.900.5595791.1651E-020.950.5498960.5612581.1362E-021.000.5407711.1048E-02h=50时，解为：0.020.980000

3、0.9803953.9471E-040.040.9607920.9615587.6599E-040.060.9423450.9434601.1148E-030.080.9246280.9260701.4422E-030.9076131.7491E-030.120.8912700.8933062.0363E-030.140.8755730.8778782.3048E-030.160.8604960.8630512.5553E-030.180.8460130.8488022.7888E-030.8321003.0058E-030.220.8187320.8219403.2073E-030.240.

4、8058890.8092833.3938E-030.260.7935470.7971133.5662E-030.280.7816850.7854103.7250E-030.7702843.8709E-030.320.7593230.7633284.0045E-030.340.7487840.7529114.1264E-030.360.7386490.7428864.2371E-030.380.7288990.7332364.3373E-030.7195184.4274E-030.420.7104900.7149984.5079E-030.440.7018000.7063794.5793E-03

5、0.460.6934310.6980734.6421E-030.480.6853710.6900674.6967E-030.6776034.7435E-030.520.6701170.6749004.7830E-030.540.6628970.6677134.8156E-030.560.6559330.6607754.8415E-030.580.6492120.6540734.8613E-030.6427234.8751E-030.620.6364540.6413374.8835E-030.640.6303950.6352824.8866E-030.660.6245370.6294224.88

6、48E-030.680.6188680.6237474.8784E-030.6133814.8676E-030.720.6080660.6129184.8528E-030.740.6029140.6077484.8341E-030.760.5979170.6027284.8119E-030.780.5930670.5978534.7863E-030.5883574.7577E-030.820.5837790.5885054.7261E-030.840.5793260.5840184.6918E-030.860.5749920.5796474.6550E-030.880.5707710.5753

7、874.6159E-030.5666564.5746E-030.920.5626410.5671724.5314E-030.940.5587210.5632074.4864E-030.960.5548900.5593304.4397E-030.980.5511440.5555354.3916E-030.5474774.3420E-03有图像看出，当步长越小，计算得到的解越逼近精确解。1.2、求解初值问题，已知精确解为：，h=0.1欧拉法改进的欧拉法预报-校正格式1.004837421.000000001.005000001.004761901.018730751.010000001.01925

8、0001.018594101.040818221.029000001.041837501.040632761.070320051.056100001.071940631.070096311.106530661.090490001.108819091.106277611.148811641.131441001.151806091.148536891.196585301.178296901.200300941.196295281.249328961.230467211.253762531.249029061.306569661.287420491.311703381.306264391.36787

9、9441.348678441.373684291.36757254欧拉法图像：改进欧拉法图像：预测-校正法图像：附录：源代码1.1、clearclcX0=0;X1=1;n=10;%更改分点数h=1/n;%步长y（1）=1;x（1）=X0;for i=1:n x（i+1）=x（i）+h; y（i+1）=y（i）+h*（x（i）*exp（-x（i）-y（i）;endx=vpa（x,6）y=vpa（yX=（X0:0.001:X1）;n=1/0.001;for（i=1:n+1） Y（i）=0.5*（X（i）2+2）*exp（-X（i）;plot（x,y,*）hold onplot（X,Y）X=X0:h:X1;Y=0.5.*（X.2+2）.*exp（-X）;Y=vpa（Yyy=abs（y-Y）1.2、欧拉法：Y=X+exp（-X）;,9）;%精确解XX=X0:0.0001:YY=XX+exp（-XX）;x（i+1）=x（i）+h;y（i+1）=y（i）+h*（-y（i）+x（i）+1）;,9）plot（XX,YY）改进的欧拉法： y（i+1）=y（i）+h*（-y（i）+x（i）+1）; y（i+1）=y（i）+0.5*h*（-y（i）+x（i）+1）+（-y（i+1）+x（i+1）+1）;预报-校正格式： for count=1:10 %预报-校正格式，迭代十次 end