数学实验基础实验报告常微分方程

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1、I.分别用Euler法和ode45解下列常微分方程并与解析解比较:(1)y=-y,y(Q)=1,1>[x,y]=euler('Fun',[0,3],1,0.1)>>[x,y]ans=01.00000.1

2、0001.10000.20001.22000.30001.36200.40001.52820.50001.72100.60001.94310.70002.19740.80002.48720.90002.81591.00003.18751.10003.60621.20004.07691.30004.60451.40005.19501.50005.85451.60006.58991.70007.40891.80008.31981.90009.33182.000010.45502.100011.70052.200013.08052.300014.60862.40

3、0016.29952.500018.16942.600020•23642.700022.52002.800025.04202.900027.82623.000030.8988ode45：>>[xzy]=ode45(1Fun'z[0,3],1)ans=01.00000.05021.05280.10051.11090.15071.17460.20101.24420.27601.35960.35101.48990.42601.63610.50101-79960.57601.98170.65102.18380.72602.40740.80102.65440.876

4、02.92640.95103.22541.02603.55351.10103.91311.17604.30651.25104.73641.32605.20561.40105.71721.47606.27441.55106.88101.62607.54061.70108.25741.77609.03591.85109.88081.926010.79742.001011.79122.076012.86832.151014.03512.226015.29862.301016.66642.376018.14662.451019.74782.526021.47962

5、.601023.35222.676025.37642.751027.56412.826029.92812.901032.48202.925733.36942.950534.27962.975235.21343.000036.1711解析解：〉〉y=dsolve('Dy=x+y','y(0)=1’,'x’)y=2*exp(x)-x-1(1)y*-0.01(/)2+2y=sin(Z),y(0)=0,y’(0)=l,0

6、]；»[t,y]=euler('Fun,,[0,5],[0,1],0.2)ode45：[t,y]=ode45(1Fun1,[0,5],[0,1])00.00010.00010.00020.00020.00050.00070.00100.00120.00250.00370.00500.00620.01250.01880.02510.03130.06270.09410.12550.15690.28190.40690.53190.65690.78190.90691.03191.15691.28191.40691.53191.65691.78191.90692.0

7、3192.15692.28192.40692.53192.65692.78192.90693.03193.15693.28193.40693.53193.65693.7819.90694.03194.15694.28194.40694.53194.65694.74274.82854.91425.000001.00000.00011.00000.00011.00000.00021.00000.00021.00000.00051.00000.00071.00000.00101.00000.00121.00000.00251.00000.00371.00000.

8、00501.00000.00621.00000.01251.000