用python实现欧拉法求原函数
2021/10/7 11:10:59
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import numpy as np import matplotlib.pyplot as plt # Problem1 h = [0.001, 0.005, 0.01, 0.05, 0.1] num = 5 / h[0] y = 1 t = 0 dy_dt = -1 tPlot = np.arange(0, 5, h[0]) yPlot = [] for i in range(int(num)): yPlot.append(y) t += h[0] y += dy_dt * h[0] dy_dt = -2*y+2-np.exp(-4*t) if i % 1000 == 999: print(t, y) plt.plot(tPlot, yPlot, label="Euler's method") yExact = (np.exp(-4*tPlot))/2-(np.exp(-2*tPlot))/2+1 plt.plot(tPlot, yExact, label="exact solution") plt.xlabel("t") plt.ylabel("y") plt.ylim(0.8, 1.05) plt.legend() plt.show() plt.plot(tPlot, yPlot, label="0.001") for i in range(4): num = 5 / h[i+1] y = 1 t = 0 dy_dt = -1 tPlot = np.arange(0, 5, h[i+1]) yPlot = [] for j in range(int(num)): yPlot.append(y) t += h[i+1] y += dy_dt * h[i+1] dy_dt = -2*y+2-np.exp(-4*t) plt.plot(tPlot, yPlot, label=h[i+1]) plt.xlabel("t") plt.ylabel("y") plt.ylim(0.8, 1.05) plt.legend() plt.show()
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