def testStableODE2(self):
iv = np.array([1.0])
h: np.float = 0.01
y = odesolvers.ExplicitEulerSolver(stableode, iv, self.t0, self.tn, h)
self.assertEqual(y[0], iv)
self.assertEqual(y[1], (y[0] - h))
def testConstantODE2(self):
iv = np.array([1.0])
h: np.float = 0.1
y = odesolvers.ExplicitEulerSolver(constantode, iv, self.t0, self.tn,
h)
self.assertEqual(y[0], iv)
self.assertEqual(y[1], (y[0] + h))
def testStiffODE2(self):
iv = np.array([1.0, 2.0])
h: np.float = 0.05
N: np.uint = np.uint(np.ceil((self.tn - self.t0) / h))
# final step
y = odesolvers.ExplicitEulerSolver(stiffode, iv, self.t0, self.tn, h)
self.assertEqual(y[0, 0], iv[0])
self.assertEqual(y[0, 1], iv[1])
self.assertGreater(np.absolute(y[N, 1] - y[0, 1]), 3)
def testMultivariableODE(self):
iv = np.array([1.0, 2.0])
h: np.float = 0.01
y = odesolvers.ExplicitEulerSolver(multivariableode, iv, self.t0,
self.tn, h)
self.assertEqual(y[0, 0], iv[0])
self.assertEqual(y[0, 1], iv[1])
self.assertEqual(y[1, 0], (iv[0] + h * (-iv[0] + iv[1])))
self.assertEqual(y[1, 1], (iv[1] - h * iv[1]))
:type t: np.float
:type x: np.array[float]
:return: Derivative of state at current time
:rtype: np.array[float]
"""
xprime = np.empty([2], float)
xprime[0] = -x[0]
xprime[1] = -100 * (x[1] - np.sin(t)) + np.cos(t)
return xprime
if __name__ == '__main__':
iv = np.array([1.0, 2.0])
t0: np.float = 0.0
tn: np.float = 1.0
h = np.array([0.01, 0.05])
for hi in np.nditer(h):
# solving the ODE
y = odesolvers.ExplicitEulerSolver(hw2ex4ode, iv, t0, tn, hi)
# plotting the results
odesolvers.plotODEsol(y[:, 0], t0, hi, 'y1(t)')
tikzplotlib.save(f'y1-{hi}.tex')
odesolvers.plotODEsol(y[:, 1], t0, hi, 'y2(t)')
tikzplotlib.save(f'y2-{hi}.tex')