def am3_tuple(function, x0, x1, y0, n):
csv_file_prey = open('results_prey.csv', 'w')
csv_file_predator = open('results_predator.csv', 'w')
prey_writer = csv.writer(csv_file_prey)
predator_writer = csv.writer(csv_file_predator)
h = (x1 - x0) / float(n)
# Inicializacao
x_k_minus_one = x0
y_k_minus_one = y0
# Primeiro ponto
x_k = x0 + h
y_k = rk2(function, x0, x_k, y0, 1)
# Segundo ponto
x_k_plus_one = x_k + h
y_k_plus_one = rk2(function, x_k, x_k_plus_one, y_k, 1)
for i in range(1, n + 1):
# Calcula temporarias para usar na conta
temp_k_minus_one = multi_tuple(- 1 / float(12), function(x_k_minus_one,
y_k_minus_one))
temp_k = multi_tuple(8 / float(12), function(x_k, y_k))
predicted_y_k_plus_one = rk2(function, x_k, x_k_plus_one, y_k, 1)
temp_k_plus_one = multi_tuple(5 / float(12), function(x_k_plus_one,
predicted_y_k_plus_one))
# Calcula novo valor de Y
new_y = add_two_tuples(y_k, multi_tuple(h, (add_many_tuples(
temp_k_minus_one, temp_k, temp_k_plus_one))))
# Atualiza os valores de X
x_k_minus_one = x_k
x_k = x_k_plus_one
x_k_plus_one = x_k_plus_one + h
# Atualiza os valores de Y
y_k_minus_one = y_k
y_k = y_k_plus_one
y_k_plus_one = new_y
# Salva nos arquivos csv
prey_writer.writerow([x_k_plus_one, y_k_plus_one[0]])
predator_writer.writerow([x_k_plus_one, y_k_plus_one[1]])
csv_file_prey.close()
csv_file_predator.close()
return y_k_plus_one
def BC_caseI(omega):
"""
Finds the value of w_1(x) at the end point. x = L = 1 (m)
"""
L = 1.
w0 = [0.0, 1.0, omega]
w = rk2(w0, 0.0, 1, 0.001, caseI)
return w[-1, 0]
def long_ball(v0, theta0):
"""
Finds the distance traveled by a baseball with the initial velocity
magnitude v0 and launched at angle theta0
Inputs
----------
v0: Initial velocity magnitude (m/s)
that0: Initial launch angle (degrees)
Output:
----------
d: Distance the ball traveled (m)
"""
theta_r = np.radians(theta0) #Convert the input angle into radians
dt = 0.01 #time step size (s)
#Initial conditions w0 = [x0, y0, vx0, vy0]
w0 = [0, 0, v0 * np.cos(theta_r), v0 * np.sin(theta_r)]
t0 = 0.0
#This is my 'flag' condition. The program will keep checking what 'done' is.
#When it gets set to True then the program will end.
done = False
while not done:
w, t = rk2(w0, t0, t0 + 2 * dt, dt,
baseball) #'tf' is set to t0+2*dt becasue I want
#to take one step and then check to see
#if we're done. The 2 is needed because
#arange doesn't end at tf but at tf-dt
w0 = w[1]
t0 = t[1] + dt
if w[1, 1] < 0: #Checks if the 'y' position is in the ground or not
done = True
if t[-1] > 30:
return print(
'Something went wrong, baseball is in the air to long')
#Baseball has it the ground in the last step
if done:
x0 = w[0, 0]
y0 = w[0, 1]
x1 = w[1, 0]
y1 = w[1, 1]
frac = y0 / (y0 - y1)
d = x0 * frac + x1 * (1 - frac)
return d
def am3_int(function, x0, x1, y0, n):
h = (x1 - x0) / float(n)
# Inicializacao
x_k_minus_one = x0
y_k_minus_one = y0
# Primeiro ponto
x_k = x0 + h
y_k = rk2(function, x0, x_k, y0, n)
# Segundo ponto
x_k_plus_one = x_k + h
y_k_plus_one = rk2(function, x_k, x_k_plus_one, y_k, n)
for i in range(1, n + 1):
# Calcula temporarias para usar na conta
temp_k_minus_one = -1 / 12 * function(x_k_minus_one, y_k_minus_one)
temp_k = 8 / 12 * function(x_k, y_k)
predicted_y_k_plus_one = rk2(function, x_k, x_k_plus_one, y_k, n)
temp_k_plus_one = 5 / 12 * function(x_k_plus_one,
predicted_y_k_plus_one)
# Calcula novo valor de Y
new_y = y_k + h * (temp_k_minus_one + temp_k + temp_k_plus_one)
# Atualiza os valores de X
x_k_minus_one = x_k
x_k = x_k_plus_one
x_k_plus_one = x_k_plus_one + h
# Atualiza os valores de Y
y_k_minus_one = y_k
y_k = y_k_plus_one
y_k_plus_one = new_y
return y_k_plus_one
## Import all of my methods
import euler
import rk2
import rk4
import se1
import se2
import sho1
import numpy as np
import matplotlib.pyplot as plt
## Execute the calculations of each one
euler.euler(euler.x, euler.v)
rk2.rk2(rk2.x, rk2.v)
rk4.rk4(rk4.x, rk4.v)
se1.se1(se1.x, se1.p)
se2.se2(se2.x, se2.p)
methods = [euler, rk2, rk4, se1, se2]
colors = ["r-", "y-", "g-", "b-", "c-"]
## Graphing area
for i, method in enumerate(methods):
plt.plot(method.t_points, method.e_points, colors[i], label=method.name)
plt.legend()
plt.xlabel("t")
plt.ylabel("total energy")
plt.title("Energy Conservation")
plt.plot(sho1.t_points, sho1.e_points, "r--", label=sho1.name)
plt.show()
from euler import eulerMethod
from rk2 import rk2
from rk4 import rk4
from rrz2 import rrz2
if __name__ == "__main__":
eulerMethod()
rk2()
rk4()
rrz2()
import picard
import newton
import rk2
if __name__ == "__main__":
picard.picard()
newton.newton()
rk2.rk2()