def test_accuracy02(self):
N = 2**10
t = np.linspace(0, 1, num=N)
y0 = np.array([1.0, 1.0]).T
exactSol = ExampleFunc02_solution(y0, t)
# Compute numerical solution:
solver = BDF6Method(N, y0, [0, 1], ExampleFunc02())
solution = solver.generate()
numericSol = []
for (time, val) in solution:
numericSol.append(val)
numericSol = np.array(numericSol).T
err = np.max(np.abs(exactSol - numericSol))
self.assertTrue(err < 5.0 * 10**(-13))
def test_accuracy02(self):
N = 2**14
t = np.linspace(0, 1, num=N)
y0 = np.array([1.0, 1.0]).T
exactSol = ExampleFunc02_solution(y0, t)
# Compute numerical solution:
ee_solver = ExplicitEuler(N, y0, [0, 1], ExampleFunc02())
solution = ee_solver.generate()
numericSol = []
for (time, val) in solution:
numericSol.append(val)
numericSol = np.array(numericSol).T
err = np.max(np.abs(exactSol - numericSol))
print(err)
self.assertTrue(err < 1.2 * 10**(-5))
def test_accuracy01(self):
N = 2**6
t = np.linspace(0, 1, num=N)
y0 = np.array([1, 1]).T
exactSol = ExampleFunc02_solution(y0, t).T
# Compute Numerical Solution:
t1 = timedomain.time()
GaussLegendre_solver = GaussLegendre(N, y0, [0, 1], ExampleFunc02())
solution = GaussLegendre_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for (time, val) in solution:
numericSol[idx, :] = val.T
idx += 1
t2 = timedomain.time()
print(t2 - t1)
err = np.max(np.abs(exactSol - numericSol))
# for i in range(N):
# print(np.abs(exactSol[i]-numericSol[i]))
self.assertTrue(err < 4 * 10**(-7))
def computeErr(N):
"""TODO: Docstring for computeErr.
:N: Number of gridpoints
:returns: err in inf norm
"""
t = np.linspace(0, 1, num=N)
# y0 = np.sin(np.linspace(-1.0*np.pi, 1.0*np.pi))
y0 = np.array([1, 1])
exactSol = ExampleFunc02_solution(y0, t).T
# Compute numerical solution:
GL_solver = GaussLegendre(N, y0, [0, 1], ExampleFunc02())
solution = GL_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for (time, val) in solution:
numericSol[idx, :] = val.T
idx += 1
err = np.max(np.abs(exactSol - numericSol))
return err