def main():
d = {}
x_0 = 1.0
y_0 = 1.0
x_n = 2.0
step_size = 0.1
list0 = euler(x_0, y_0, x_n, 0.1)
list1 = euler(x_0, y_0, x_n, 0.05)
list2 = euler(x_0, y_0, x_n, 0.025)
list3 = improved_euler(x_0, y_0, x_n, 0.1)
list4 = improved_euler(x_0, y_0, x_n, 0.05)
list5 = improved_euler(x_0, y_0, x_n, 0.025)
for i in np.arange(x_0, x_n + step_size, step_size):
y0 = [point[1] for point in list0 if math.isclose(point[0], i)][0]
y1 = [point[1] for point in list1 if math.isclose(point[0], i)][0]
y2 = [point[1] for point in list2 if math.isclose(point[0], i)][0]
y3 = [point[1] for point in list3 if math.isclose(point[0], i)][0]
y4 = [point[1] for point in list4 if math.isclose(point[0], i)][0]
y5 = [point[1] for point in list5 if math.isclose(point[0], i)][0]
y6 = exact(i)
entry = [y0, y1, y2, y3, y4, y5, y6]
d[i] = entry
with pd.option_context('display.precision', 9):
datFrame = pd.DataFrame.from_dict(d, orient='index',
columns=['h = 0.1', 'h = 0.05',
'h = 0.025', 'h = 0.1',
'h = 0.05', 'h = 0.025',
'Exact'])
print(datFrame.to_latex())
def test_euler_20(self):
self.assertEqual(euler(0, 0, 0, 0.1), (0, 0))
def test_euler_10(self):
self.assertEqual(euler(0.2, 0, 1, 0.1),
(0.9999999999999999, 0.3522851585103483))
def test_euler_50(self):
self.assertEqual(euler(0, 0, 0.1, 0.0001),
(0.10000000000000184, 0.0009990199006611853))
def test_euler_40(self):
self.assertEqual(euler(-5, 2.1, 0, 0.1),
(4.200000000000001, 0.42884703254758155))
def test_euler_30(self):
self.assertEqual(euler(0, 0, -1, 0.1),
(0.9999999999999999, 0.09117146625980643))
while 1:
try:
y0 = float(input("Enter y0 (from -1000000000 to 1000000000): "))
if y0 < -1000000000 or y0 > 1000000000:
print("You entered wrong data\n")
else:
break
except ValueError:
print("You entered wrong data\n")
while 1:
try:
h = float(input("Enter step (from 0.0000001 to 10): "))
if h < 0.0000001 or h > 10 or h > abs(xn - x0):
print("You entered wrong data\n")
else:
break
except ValueError:
print("You entered wrong data\n")
if xn < x0:
h = -h
x, y = euler(y0, x0, xn, h)
print(
"\nSolution of differential equation y' = 0.2*x + y^2 with initial condition y(",
x0, ") = ", y0, " :")
print("\n x = ", x)
print("\n y = ", y)