常微分方程数值解实验报告

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1、常微分数值解实验报告《常微分方程数值解》实验报告姓名：张彬班级：信计092学号：0909290229-7-常微分数值解实验报告实验目的：应用前面实验程序求解常微分方程初值问题，通过改变的初值，重点了解Euler方法及其改进方法的稳定性及收敛性实验内容：；求满足初值条件x=2，y=2的解；x∈[2，4]，步长h=0.05，并通过数值与图像进行比较。实验原理：1.前述几种数值计算方法对于初值及步长的选取都有依赖性。2.对于无法获得精确解的常微分方程初值问题，更需要分析计算结果的稳定性与收敛性。实验结果：h=0.05x=2y=2欧拉法表1Yend=自变量欧拉值精确解误差估计22202.051.9

2、659341.964661-0.000652.11.9294291.927094-0.001212.151.8909741.887814-0.001672.21.851111.847387-0.002012.251.8104181.806424-0.002212.31.7695281.765583-0.002232.351.7291091.725564-0.00205-7-常微分数值解实验报告2.41.689871.68711-0.001642.451.6525581.651004-0.000942.51.6179561.6180636.64E-052.551.5868741.589137

3、0.0014242.61.5601521.5651040.0031642.651.5386511.5468610.0053082.71.5232461.5353260.0078682.751.5148261.5314220.0108372.81.514281.5360760.0141892.851.5224931.5502050.0178772.91.5403351.5747110.021832.951.5686551.6104680.02596331.6082651.6583060.0301763.051.6599321.7190050.0343653.11.7243641.793278

4、0.0384293.151.8021991.8817550.0422773.21.8939871.984970.0458363.252.000182.1033430.0490473.32.1211142.2371680.0518753.352.2569962.3865910.0543013.42.4078892.55160.0563223.452.5736972.7320090.0579473.52.7541552.9274410.0591943.552.9488113.1373220.0600873.63.1570223.3608670.0606533.653.3779433.59707

5、40.0609193.73.6105223.8447220.0609153.753.8534974.1023690.0606663.84.1053984.3683580.0601973.854.3645524.6408210.059533.94.629094.9176970.0586873.954.8969655.1967470.05768645.1659645.4755780.056545-7-常微分数值解实验报告图1改进欧拉法：表2Yend=自变量欧拉改进法精确解误差估计22202.051.9647141.964661-2.7E-052.11.9272041.927094-5.8E-0

6、52.151.8879861.887814-9.1E-052.21.8476221.847387-0.000132.251.8067231.806424-0.000172.31.7659471.765583-0.000212.351.7259931.725564-0.000252.41.6876041.68711-0.00029-7-常微分数值解实验报告2.451.651561.651004-0.000342.51.6186781.618063-0.000382.551.5898061.589137-0.000422.61.565821.565104-0.000462.651.547619

7、1.546861-0.000492.71.5361161.535326-0.000512.751.5322341.531422-0.000532.81.5368991.536076-0.000542.851.5510271.550205-0.000532.91.5755171.574711-0.000512.951.6112411.610468-0.0004831.659031.658306-0.000443.051.7