def calculate__one_dimensional__wave_equation__boundary_task(animation_plot, coef, y__x_tzero, dydt__x_tzero, external_influences, \
boundary_function__xzero, boundary_function__xeql):
y__x_tzero = calculate(y__x_tzero)
dydt__x_tzero = calculate(dydt__x_tzero)
external_influences = calculate(external_influences)
sqrt_coef = coef**0.5
def function(x, t, y_previous, y):
n = len(x) - 1
dx = x[1] - x[0]
dt = 0.05
gamma2 = (dt / dx * sqrt_coef)**2
if y is None:
y = [0] * (n + 1)
for i in range(0, n + 1):
y[i] = y__x_tzero(x[i],
t) + dt**2 * external_influences(x[i], t)
return y
if y_previous is not None:
y_next = [0] * (n + 1)
for i in range(1, n):
y_next[i] = 2 * y[i] - y_previous[i] + \
gamma2 * (y[i + 1] - 2 * y[i] + y[i - 1]) + \
dt ** 2 * external_influences(x[i], t)
else:
y_next = [0] * (n + 1)
for i in range(1, n):
y_next[i] = y[i] + \
gamma2 / 2 * (y[i + 1] - 2 * y[i] + y[i - 1]) + \
dt * dydt__x_tzero(x[i], t) + \
dt ** 2 / 2 * external_influences(x[i], t)
y_next[0] = boundary_function__xzero(x[0], t, dt, y[0])
y_next[n] = boundary_function__xeql(x[n], t, dt, y[n])
return y_next
animation_plot.clean_result_part()
y_previous = y = None
for t in animation_plot.get_t():
animation_plot.y.append(
function(animation_plot.get_x(), t, y_previous, y))
y_previous, y = y, animation_plot.y[-1]
return animation_plot
def get_first_boundary_function(y__x_t):
y__x_t = calculate(y__x_t)
def foo(x, t, dt, y):
return y__x_t(x, t)
return foo
def get_second_boundary_function(dydx__x_t):
dydx__x_t = calculate(dydx__x_t)
def foo(x, t, dt, y):
return dydx__x_t(x, t) * dt + y
return foo
def get_third_boundary_function(a__x, b__x, third_boundary_function__x):
third_boundary_function__x = calculate(third_boundary_function__x)
def foo(x, t, dt, y):
return (third_boundary_function__x(x, t) * dt + y) / \
(dt * a__x + b__x)
return foo
def calculate__one_dimensional__heat_equation__cauchy(animation_plot, coef,
y__x_tzero,
external_influences):
y__x_tzero = calculate(y__x_tzero)
external_influences = calculate(external_influences)
sqrt_coef = coef**0.5
def function(x, t, y):
y_next = None
n = len(x) - 1
dx = x[1] - x[0]
dt = 0.05
gamma2 = dt * (1. / dx * sqrt_coef)**2
if y is None:
y = [0] * (n + 1)
for i in range(0, n + 1):
y[i] = y__x_tzero(x[i], t) + dt * external_influences(x[i], t)
return y
y_next = [0] * (n + 1)
for i in range(1, n):
y_next[i] = y[i] + \
gamma2 * (y[i + 1] - 2 * y[i] + y[i - 1]) + \
dt * external_influences(x[i], t)
i = 0
y_next[0] = y_next[1]
i = n
y_next[n] = y_next[n - 1]
y = y_next
return y_next
animation_plot.clean_result_part()
y = None
for t in animation_plot.get_t():
y = function(animation_plot.get_x(), t, y)
animation_plot.y.append(y)
return animation_plot
def gui_main_one_dimensional__heat_equation__homogeneous(
animation_plot, coef, y__x_tzero):
function = calculate(
one_dimensional__heat_equation__homogeneous(coef, y__x_tzero))
animation_plot.clean_result_part()
for t in animation_plot.get_t():
next_y = function(animation_plot.get_x(), t)
animation_plot.y.append(next_y)
return animation_plot
def gui_main_one_dimensional__wave_equation__homogeneous(
animation_plot, coef, y__x_tzero, dydt__x_tzero):
coef, y__x_tzero, dydt__x_tzero = input_to_sympy(coef, y__x_tzero,
dydt__x_tzero)
function = calculate(
one_dimensional__wave_equation__homogeneous(coef, y__x_tzero,
dydt__x_tzero))
animation_plot.clean_result_part()
for t in animation_plot.get_t():
animation_plot.y.append(function(animation_plot.get_x(), t))
return animation_plot