def example_2(c, xc, tc):
"""
example #2: r = 0.83333 (example 10.3, table 10.4)
:param c: coefficient
:param xc: count of point on Ox axis
:param tc: count of point on time axis
"""
Solve.solve_exercise(lambda: ExplicitScheme.solve(
lambda x: 4 * x - 4 * x ** 2, 0, 0,
1, 0.33333, c, xc, tc
), plot_projection_res=True, print_res=True, ain=100)
def example(c, xc, tc):
"""
example #1: (example 10.4, table 10.5)
:param c: coefficient
:param xc: count of point on Ox axis
:param tc: count of point on time axis
"""
Solve.solve_exercise(lambda: ExplicitScheme.solve(
lambda x: math.sin(math.pi * x) + math.sin(3 * math.pi * x), 0, 0,
1, 0.1, c, xc, tc
), plot_projection_res=True, print_res=True, ain=100)
def ex2(h, tol, max_steps):
"""
example #2: (example 10.6, table 10.7)
:param h: step
:param tol: maximum delta
:param max_steps: max count of steps
"""
Solve.solve_exercise(lambda: Dirichlel.solve_diff(
lambda x, u, i, j: u[i, j + 1], lambda x: 180,
lambda x: 80, lambda x: 0,
4, 4, h, tol, max_steps
), plot_projection_res=True, ain=15, print_res=True)
def ex1(h, tol, max_steps):
"""
example #1: (example 10.5, table 10.6)
:param h: step
:param tol: maximum delta
:param max_steps: max count of steps
"""
Solve.solve_exercise(lambda: Dirichlel.solve(
lambda x: 20, lambda x: 180,
lambda x: 80, lambda x: 0,
4, 4, h, tol, max_steps
), plot_projection_res=True, ain=15, print_res=True)
def ex2(h, tol, max_steps):
"""
example #2: (example 10.6, table 10.7)
:param h: step
:param tol: maximum delta
:param max_steps: max count of steps
"""
Solve.solve_exercise(lambda: Dirichlel.solve_diff(
lambda x, u, i, j: u[i, j + 1], lambda x: 180, lambda x: 80, lambda
x: 0, 4, 4, h, tol, max_steps),
plot_projection_res=True,
ain=15,
print_res=True)
def ex1(h, tol, max_steps):
"""
example #1: (example 10.5, table 10.6)
:param h: step
:param tol: maximum delta
:param max_steps: max count of steps
"""
Solve.solve_exercise(
lambda: Dirichlel.solve(lambda x: 20, lambda x: 180, lambda x: 80,
lambda x: 0, 4, 4, h, tol, max_steps),
plot_projection_res=True,
ain=15,
print_res=True)
def ex3(c, a, l, msc, xc, tc):
Solve.solve_exercise(lambda: FiniteDifference.solve(
lambda z: a * math.sin(math.pi / l * msc * z),
lambda z: 0,
1, 0.5, c, xc, tc
), plot_projection_res=True, ain=15)
def analytic_solve(func, x_boundary, t_boundary, x_points_count, t_points_count):
x_step = x_boundary / (x_points_count - 1)
t_step = t_boundary / (t_points_count - 1)
x = [i * x_step for i in range(x_points_count)]
t = [i * t_step for i in range(t_points_count)]
u = pylab.zeros((t_points_count, x_points_count))
for i in range(t_points_count):
for j in range(x_points_count):
u[i][j] = func(x[j], t[i])
return x, t, u
Solve.solve_exercise(lambda: analytic_solve(
lambda z, temp: a * math.sin(math.pi / l * z * msc) * math.cos(math.pi / l * msc * c * temp),
1, 0.5, xc, tc
), plot_projection_res=True, ain=15)
def ex3(c, a, l, msc, xc, tc):
Solve.solve_exercise(lambda: FiniteDifference.solve(
lambda z: a * math.sin(math.pi / l * msc * z), lambda z: 0, 1, 0.5,
c, xc, tc),
plot_projection_res=True,
ain=15)
def analytic_solve(func, x_boundary, t_boundary, x_points_count,
t_points_count):
x_step = x_boundary / (x_points_count - 1)
t_step = t_boundary / (t_points_count - 1)
x = [i * x_step for i in range(x_points_count)]
t = [i * t_step for i in range(t_points_count)]
u = pylab.zeros((t_points_count, x_points_count))
for i in range(t_points_count):
for j in range(x_points_count):
u[i][j] = func(x[j], t[i])
return x, t, u
Solve.solve_exercise(lambda: analytic_solve(
lambda z, temp: a * math.sin(math.pi / l * z * msc) * math.cos(
math.pi / l * msc * c * temp), 1, 0.5, xc, tc),
plot_projection_res=True,
ain=15)
def ex2(c, xc, tc):
Solve.solve_exercise(lambda: FiniteDifference.solve(
lambda z: z if 0 <= z <= 3 / 5 else 1.5 - 1.5 * z, lambda z: 0, 1,
0.5, c, xc, tc),
plot_projection_res=True,
ain=150)
def ex1(c, xc, tc):
Solve.solve_exercise(lambda: FiniteDifference.solve(
lambda z: math.sin(math.pi * z) + math.sin(2 * math.pi * z), lambda
z: 0, 1, 0.5, c, xc, tc),
plot_projection_res=True,
ain=15)
def ex2(c, xc, tc):
Solve.solve_exercise(lambda: FiniteDifference.solve(
lambda z: z if 0 <= z <= 3 / 5 else 1.5 - 1.5 * z,
lambda z: 0,
1, 0.5, c, xc, tc
), plot_projection_res=True, ain=150)
def ex1(c, xc, tc):
Solve.solve_exercise(lambda: FiniteDifference.solve(
lambda z: math.sin(math.pi * z) + math.sin(2 * math.pi * z),
lambda z: 0,
1, 0.5, c, xc, tc
), plot_projection_res=True, ain=15)