def test_analytic():
#
# Test case: Solve u' = -u + 1, u(0) = 0.
#
# Compare the numerical solution given by
# solver_leapfrog() with the analytic
# solution u_e(t) = 1 - exp(-t).
#
def a(t):
return 1.0
def b(t):
return 1.0
# Solve numerically
u, t = lf.solver_leapfrog(I=0.0, a=a, b=b, \
T=1.0, dt=1.0E-6, \
theta=0.0)
# Analytic expression
u_e = 1.0 - np.exp(-t)
# Maximum difference
diff = np.abs(u - u_e).max()
# Test approximative equality
nt.assert_almost_equal(diff, 0, delta=1E-12)
def test_linear_solution():
#
# Method of manufactured solution:
# Test solver_leapfrog() with a
# linear solution u_e(t) = ct + I.
#
# Exact solution
def linear_solution(t):
return c*t + I
def a(t):
return mt.sin(t) # Arbitrary function
def b(t):
return c + a(t)*linear_solution(t)
c = 0.4
I = 3.0
# Solve numerically
u, t = lf.solver_leapfrog(I=I, a=a, b=b, \
T=1.2, dt=1.0E-6, \
theta=0.0)
# Analytic expression
u_e = linear_solution(t)
# Maximum difference
diff = np.abs(u-u_e).max()
# Test approximative equality
nt.assert_almost_equal(diff, 0, delta=1E-10)
def test_linear_solution():
#
# Method of manufactured solution:
# Test solver_leapfrog() with a
# linear solution u_e(t) = ct + I.
#
# Exact solution
def linear_solution(t):
return c * t + I
def a(t):
return mt.sin(t) # Arbitrary function
def b(t):
return c + a(t) * linear_solution(t)
c = 0.4
I = 3.0
# Solve numerically
u, t = lf.solver_leapfrog(I=I, a=a, b=b, \
T=1.2, dt=1.0E-6, \
theta=0.0)
# Analytic expression
u_e = linear_solution(t)
# Maximum difference
diff = np.abs(u - u_e).max()
# Test approximative equality
nt.assert_almost_equal(diff, 0, delta=1E-10)
def test_analytic():
#
# Test case: Solve u' = -u + 1, u(0) = 0.
#
# Compare the numerical solution given by
# solver_leapfrog() with the analytic
# solution u_e(t) = 1 - exp(-t).
#
def a(t):
return 1.0
def b(t):
return 1.0
# Solve numerically
u, t = lf.solver_leapfrog(I=0.0, a=a, b=b, \
T=1.0, dt=1.0E-6, \
theta=0.0)
# Analytic expression
u_e = 1.0 - np.exp(-t)
# Maximum difference
diff = np.abs(u-u_e).max()
# Test approximative equality
nt.assert_almost_equal(diff, 0, delta=1E-12)
