def testMultivariableODE(self): h : np.float = 0.01; y = odesolvers.ThetaMethod(multivariableode, self.iv, self.t0, self.tn, h, self.theta, multivariableodeJ); self.assertEqual(y[0,0],self.iv[0]); self.assertEqual(y[0,1],self.iv[1]); self.assertLess(y[1,1], y[0,1]);
def testErrorHandling(self):
iv = np.array([0.0])
# negative time step
with self.assertRaises(ValueError):
odesolvers.ThetaMethod(stableode, iv, self.t0, self.tn, -0.1, 1)
# zero time step
with self.assertRaises(ValueError):
odesolvers.ThetaMethod(stableode, iv, self.t0, self.tn, 0.0, 1)
# time flowing negatively
with self.assertRaises(ValueError):
odesolvers.ThetaMethod(stableode, iv, self.tn, self.t0, 0.1, 1)
# theta out of bounds
with self.assertRaises(ValueError):
odesolvers.ThetaMethod(stableode, iv, self.t0, self.tn, 0.1, 2)
# Negative numerical tolerance
with self.assertRaises(ValueError):
odesolvers.ThetaMethod(stableode,
iv,
self.t0,
self.tn,
0.1,
0.5,
TOL=-0.1)
# Negative number of Newton iteration steps
with self.assertRaises(ValueError):
odesolvers.ThetaMethod(stableode,
iv,
self.t0,
self.tn,
0.1,
0.5,
NEWTITER=-2)
# Automatic differentiation
with self.assertRaises(NotImplementedError):
odesolvers.ThetaMethod(stableode, iv, self.t0, self.tn, 0.1, 0)
def testStiffODENotConvergent(self): h : np.float = 0.05; N : np.uint = np.uint(np.ceil((self.tn - self.t0)/h)); # final step y = odesolvers.ThetaMethod(stiffode, self.iv, self.t0, self.tn, h, 0.8, stiffodeJ); self.assertEqual(y[0,0],self.iv[0]); self.assertEqual(y[0,1],self.iv[1]); self.assertGreater(np.absolute(y[N,1]-y[0,1]),3);
return df
if __name__ == '__main__':
# Problem 1
iv = np.array([1.0, 2.0])
t0: np.float = 0.0
tn: np.float = 1.0
theta = np.array([0, 0.5, 1])
h = np.array([0.01, 0.05])
for thetai in np.nditer(theta):
for hi in np.nditer(h):
y = odesolvers.ThetaMethod(hw4ex1ode1, iv, t0, tn, hi, thetai,
hw4ex1Jacobian1)
# plotting the results
odesolvers.plotODEsol(y[:, 0], t0, hi, 'y1(t)')
tikzplotlib.save(f'problem1-y1-step-{hi}-theta-{thetai}.tex')
odesolvers.plotODEsol(y[:, 1], t0, hi, 'y2(t)')
tikzplotlib.save(f'problem1-y2-step-{hi}-theta-{thetai}.tex')
# Problem 2
iv = np.array([10, 10])
tn = 100
h = np.array([0.1, 0.001])
for thetai in np.nditer(theta):
for hi in np.nditer(h):