Heuns method in Python - Printable Version +- Python Forum (https://python-forum.io) +-- Forum: Python Coding (https://python-forum.io/forum-7.html) +--- Forum: Data Science (https://python-forum.io/forum-44.html) +--- Thread: Heuns method in Python (/thread-5728.html) |
Heuns method in Python - auting82 - Oct-18-2017 Hi I am testing some ready made code in python and comapring forward eueler method and Heuns method. Since Heuns method is more precise, the full blue graph representing Heuns method approximation should be closer to the true graph. Does anybody see any errors here ? from numpy import linspace, zeros, exp from ode_FE import ode_FE import matplotlib.pyplot as plt def ode_Heun(f, U_0, dt, T): N_t = int(round(float(T)/dt)) u = zeros(N_t+1) t = linspace(0, N_t*dt, len(u)) u[0] = U_0 for n in range(N_t): u_star = u[n] + dt*f(u[n],t[n]) u[n+1] = u[n] + 0.5*dt*(f(u[n],t[n]) + f(u_star,t[n])) return u, t def demo_ode_Heun(): """Test case: u’ = u, u(0) = 1""" def f(u,t): return u u_Heun, t = ode_Heun(f=f, U_0=1, dt=0.5, T=6) u_FE, t = ode_FE(f=f, U_0=1, dt=0.5, T=6) fig = plt.figure() l1, l2, l3 = plt.plot(t, u_Heun,'b-', t, u_FE,'b--', t, exp(t),'r--') fig.legend((l1, l2, l3), ('H', 'FE', 'true'), 'upper left') plt.xlabel('t') plt.show() if __name__ == '__main__': demo_ode_Heun() |