index=0,
analytical_solution=ho_solution,
dt=dt,
maxt=maxt)
graphs.plot_compare_methods(ho, (0, 1),
index=0,
analytical_solution=ho_solution,
integrators=[
ode.euler_2, ode.runge_kutta_4,
symplectic.verlet,
symplectic.euler_1_modified_x
],
dt=dt,
maxt=maxt)
graphs.plot_compare_steps(ho, (0, 1),
ode.euler_1,
analytical_solution=ho_solution,
maxt=maxt)
symplectic.plot_energy(ho, (0, 1), energy_function=ho_energy, dt=dt, maxt=maxt)
symplectic.plot_energy(
ho, (0, 1),
energy_function=ho_energy,
dt=dt,
maxt=maxt,
integrators=[ode.euler_2, ode.runge_kutta_4, symplectic.verlet])
graphs.plot_cummulative_error(ho, (0, 1),
ho_solution,
index=0,
integrators=[
ode.euler_1, ode.euler_2, ode.runge_kutta_4,
import numpy as np
import ode
import graphs
def relaxation(y, t):
""" Derivatives for the relaxation system """
return -y
def analytical_solution(t):
return np.exp(-t)
graphs.plot_compare_methods(relaxation, 1, analytical_solution=analytical_solution, dt=0.5)
graphs.plot_compare_steps(relaxation, 1, ode.euler_1, analytical_solution=analytical_solution)
graphs.plot_compare_steps(relaxation, 1, ode.euler_2, analytical_solution=analytical_solution)
graphs.plot_compare_steps(relaxation, 1, ode.runge_kutta_4, analytical_solution=analytical_solution)
graphs.plot_cummulative_error(relaxation, 1, analytical_solution)
maxt = 20
graphs.plot_compare_methods(exp, (1, -1),
index=0,
analytical_solution=exp_solution,
dt=dt,
maxt=maxt)
graphs.plot_compare_methods(exp, (1, -1),
index=0,
analytical_solution=exp_solution,
integrators=[
ode.euler_1, ode.euler_2, ode.runge_kutta_4,
symplectic.verlet,
symplectic.euler_1_modified_x
],
dt=dt,
maxt=maxt)
graphs.plot_compare_steps(exp, (1, -1),
ode.euler_1,
analytical_solution=exp_solution,
maxt=maxt)
graphs.plot_compare_steps(exp, (1, -1),
ode.euler_2,
analytical_solution=exp_solution,
maxt=maxt)
graphs.plot_compare_steps(exp, (1, -1),
symplectic.verlet,
analytical_solution=exp_solution,
maxt=maxt)