def test_convergence01(self):
Narr = [2**n for n in range(3, 12)]
err = []
for N in Narr:
t = np.linspace(0, 1, num=N)
y0 = np.array([np.pi])
exactSol = ExampleFunc01_solution(y0, t).T
# Compute numerical solution:
RK4_solver = RK4(N, y0, [0, 1], ExampleFunc01())
solution = RK4_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for (time, val) in solution:
numericSol[idx] = val
idx += 1
err.append(np.max(np.abs(exactSol-numericSol)))
isOkay = True
ratio = []
for i in range(1, len(err)):
ratio.append((err[i-1] / err[i]))
if ratio[i - 1] < 0.9*(2**4):
isOkay = False
print((ratio[i-1], err[i]))
self.assertTrue(isOkay)
def test_accuracy01(self):
N = 10**5
t = np.linspace(0, 1, num=N)
y0 = np.array([np.pi])
exactSol = ExampleFunc01_solution(y0, t).T
# Compute numerical solution:
ee_solver = ExplicitEuler(N, y0, [0, 1], ExampleFunc01())
solution = ee_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for (time, val) in solution:
numericSol[idx] = val
idx += 1
err = np.max(np.abs(exactSol - numericSol))
self.assertTrue(err < 1.2 * 10**(-5))
def test_accuracy01(self):
N = 2**10
t = np.linspace(0, 1, num=N)
y0 = np.array([np.pi])
exactSol = ExampleFunc01_solution(y0, t).T
# Compute numerical sol:
mpr_solver = MidPointRule(N, y0, [0, 1], ExampleFunc01())
solution = mpr_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for (time, val) in solution:
numericSol[idx] = val
idx += 1
err = np.max(np.abs(exactSol - numericSol))
print(err)
self.assertTrue(err < 4.0 * 10**(-7))
def test_accuracy01(self):
N = 10**3
t = np.linspace(0, 1, num=N)
# y0 = np.sin(np.linspace(-1.0*np.pi, 1.0*np.pi))
y0 = np.array([np.pi])
exactSol = ExampleFunc01_solution(y0, t).T
# Compute numerical solution:
ie_solver = ImplicitEuler(N, y0, [0, 1], ExampleFunc01())
solution = ie_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for (time, val) in solution:
numericSol[idx] = val
idx += 1
err = np.max(np.abs(exactSol - numericSol))
print(err)
self.assertTrue(err < 4.0*10**(-7))
def test_accuracy01(self):
N = 10**3
t = np.linspace(0, 1, num=N)
# y0 = np.sin(np.linspace(-1.0*np.pi, 1.0*np.pi))
y0 = np.array([np.pi])
exactSol = ExampleFunc01_solution(y0, t).T
# Compute numerical solution:
bdf6_solver = BDF6Method(N, y0, [0, 1], ExampleFunc01())
solution = bdf6_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for val in solution:
numericSol[idx] = val[1]
idx += 1
err = np.max(np.abs(exactSol - numericSol))
# BDF6 does not work correctly :/
print("Error = {}".format(err))
self.assertTrue(err < 10**(-12))
def test_accuracy01(self):
N=2**10
t=np.linspace(0,1,num=N)
y0=np.array([np.pi])
exactSol = ExampleFunc01_solution(y0,t).T
# Compute Numerical Solution:
t1=timedomain.time()
GaussLegendre_solver=GaussLegendre(N, y0, [0,1],ExampleFunc01())
solution= GaussLegendre_solver.generate()
numericSol= np.zeros_like(exactSol)
idx = 0
for (time,val) in solution:
numericSol[idx] = val
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.pi]
exactSol = ExampleFunc01_solution(y0, t).T
# Compute numerical solution:
mpr_solver = MidPointRule(N, y0, [0, 1], ExampleFunc01())
solution = mpr_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for (time, val) in solution:
numericSol[idx] = val
idx += 1
err = np.max(np.abs(exactSol - numericSol))
return err
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([np.pi])
exactSol = ExampleFunc01_solution(y0, t).T
# Compute numerical solution:
bdf6_solver = BDF6Method(N, y0, [0, 1], ExampleFunc01())
solution = bdf6_solver.generate()
numericSol = np.zeros_like(exactSol)
idx = 0
for val in solution:
numericSol[idx] = val[1]
idx += 1
err = np.max(np.abs(exactSol - numericSol))
return err