def draw_all(n):
plt.close()
x_points = np.linspace(0, 1, n, endpoint=True)
y_0 = 0.0
right_boundary = e - 1.0/e + L # = y'(1)
for method, color in [
(explicit_euler, 'r8-'),
(recount_euler, 'rs-'),
(runge_kutta, 'yd-'),
]:
last_m = 0
y_points = method(x_points, 1.0 / n, y_0, last_m, f)
next_m = get_next_m(x_points, f, method, y_0, right_boundary, last_m, 1.0 / n)
while abs(next_m - last_m) > 0.01:
y_points = method(x_points, 1.0 / n, y_0, next_m, f)
last_m = next_m
next_m = get_next_m(x_points, f, method, y_0, right_boundary, last_m, 1.0 / n)
plt.plot(x_points, y_points, color, label=method.__doc__)
plt.plot(x_points, list(map(real_func, x_points)), 'b*-', label='Original')
plt.plot(x_points, progon(x_points, right_boundary, 1.0 / n, L), "r*-", label="progon")
legend = plt.legend(loc='upper left', shadow=True, fontsize='x-large')
legend.get_frame().set_facecolor('#00FFCC')
mng = plt.get_current_fig_manager()
mng.window.state('zoomed')
# mng.full_screen_toggle()
plt.show()
def main():
n = 30 # int(sys.argv[1])
x_points = np.linspace(0, 1, n+1, endpoint=True)
y_0 = 0
right_boundary = e - 1.0/e + L
h = 1.0/n
colors = ["blue", "purple", "orange", "green"]
methods = [
{"f": explicit_euler, "name": "euler"},
{"f": recount_euler, "name": "euler with recount"},
{"f": runge_kutta, "name": "Runge-Kutta"}
]
p = figure(title="", plot_width=1100, plot_height=600)
y_points = list(map(real_func, x_points))
p.line(x=x_points, y=y_points, color="black", legend="real", line_width=2)
y_points = progon(x_points, right_boundary, h, L)
p.line(x=x_points, y=y_points, color="red", legend="progon", line_width=2)
for i in range(len(methods)):
# y_points = real_func_method(x_points)
last_m = 0
y_points = [methods[i]["f"](x_points, h, y_0, last_m, f)]
next_m = get_next_m(x_points, f, methods[i]["f"], y_0, right_boundary, last_m, h)
while abs(next_m - last_m) > 0.01:
y_points.append(methods[i]["f"](x_points, h, y_0, next_m, f))
last_m = next_m
next_m = get_next_m(x_points, f, methods[i]["f"], y_0, right_boundary, last_m, h)
p.line(x=x_points, y=y_points[-1], color=colors[i], legend=methods[i]["name"])
output_file("{0}_points.html".format(n))
p.legend.orientation = "top_left"
show(p)