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Week5: Wrap up: plot accuracy/stepsize (needs fix)

master
Eric Teunis de Boone 2 years ago
parent
commit
3111c8c022
  1. 76
      week5/ex1.py

76
week5/ex1.py

@ -75,6 +75,7 @@ def mk_phi_AB4(f, phi_short = None):
##############
def integrator(x, y_0, phi, y_i = None ):
x = np.asarray(x)
if isinstance(y_0, (list,np.ndarray)):
y_0 = np.asarray(y_0)
else:
@ -236,16 +237,85 @@ def plot_integration_errors():
pyplot.xlabel("x")
pyplot.ylabel("absolute error $|\\bar{y} - y|$")
pyplot.title("absolute error between an approach and the exact solution")
pyplot.legend()
pyplot.show()
def accuracy_per_stepsize( debug=True ):
stepsizes = np.asarray([1e-1, 1e-2, 1e-3, 1e-5])
# define the problem to be solved
test_func = lambda x,y: x
exact_sol = lambda x: np.exp(x)
# set domain and intial value
x_min = 0
x_max = 2
y_0 = 1
exact_end = exact_sol(x_max)
# define the schemes to use
schemes = [
["Euler", mk_phi_euler, 1],
["Collatz", mk_phi_euler_mod, 1],
["Heun", mk_phi_heun, 1],
["RK4", mk_phi_rk4, 1],
["AB3", mk_phi_AB3, 3],
["AB4", mk_phi_AB4, 4],
]
# get max steps needed for the multistep schemes
max_steps = 0
for _, _, steps in schemes:
if steps > max_steps:
max_steps = steps
# pre calculate for multistep integrations
y_init = np.zeros((len(stepsizes),1))# Note the dimensionality of y_0
max_steps += 1
for i, h in enumerate(stepsizes):
x = x_min + np.linspace(0, h * max_steps, max_steps, True)
# Note the dimensionality of y_0
# TODO: fix up this ugliness
z = integrator(x[:4], y_0, mk_phi_rk4(test_func))
y_init[i] = z[1,:]
# plot schemes
from matplotlib import pyplot
pyplot.subplots()
for name, scheme, steps in schemes:
diffs = np.zeros(len(stepsizes))
if debug:
print("Calculating {}".format(name))
for i, h in enumerate(stepsizes):
N = int(abs(x_max-x_min)/h)
x = np.linspace(x_min, x_max, N, True)
y = integrator(x, y_0, scheme(test_func), y_init[:steps])
diffs[i] = np.abs(exact_end - [-1])
pyplot.plot(stepsizes, diffs, '--o', label=name)
pyplot.xlabel('Stepsize $h$')
pyplot.ylabel('Absolute Error')
pyplot.title('Absolute error at the end of integration')
pyplot.legend()
pyplot.show()
def pendulum_problem():
pass
if __name__ == "__main__":
np.random.seed(0)
#test_integrator_singlestep()
test_integrator_singlestep()
#test_integrator_multistep()
plot_integration_errors()
#plot_integration_errors()
#accuracy_per_stepsize()