def u_next_lax_wendroff(u_last, u_halfstep, delta_t, delta_x, j, time,
position):
u_halfstep[j] = u_next_half_step(u_last, delta_t, delta_x, j, time,
position)
return u_last[j] - delta_t/delta_x*(func.f(u_halfstep[j])-func.f(u_halfstep[j-1])) \
+ delta_t*func.g(u_halfstep, delta_x, j)\
+ delta_t/2*(func.s(time, position, u_halfstep, j)\
+ func.s(time, position, u_halfstep, j-1))
def forward_step(self, x):
"""Return z_k = g(a_k, a_k+1) values for this layer (as a vector)"""
a_q = self.layer_output(x)
# Apply transfer function
a_q_even = a_q[::2]
a_q_odd = a_q[1::2]
z = func.g(a_q_even, a_q_odd)
assert len(z) == self.h, "Invalid size of output vector (z)"
return z
def test_g():
g()
def u_next_upwind(u_last, delta_t, delta_x, j, time, position):
return u_last[j] - delta_t/delta_x*(func.f(u_last[j])-func.f(u_last[j-1])) \
+ delta_t*func.g(u_last, delta_x, j)\
+ delta_t*func.s(time, position, u_last, j)
def u_next_half_step(u_last, delta_t, delta_x, j, time, position):
return (u_last[j+1] + u_last[j] - delta_t /delta_x*(func.f(u_last[j+1]) - func.f(u_last[j])) \
+ delta_t*func.g(u_last, delta_x, j)
+ delta_t/2*(func.s(time, position, u_last, j+1)+func.s(time, position, u_last, j)))/2
def u_approx_mac_cormack(u_last, delta_t, delta_x, j, time, position):
return u_last[j] - delta_t/delta_x*(func.f(u_last[j]) - func.f(u_last[j-1])) \
+ delta_t*func.g(u_last, delta_x, j)\
+ delta_t*func.s(time, position+delta_x, u_last, j)
def u_next_mac_cormack(u_last, u_approx, delta_t, delta_x, j, time, position):
return (u_approx[j]+u_last[j]- (delta_t)/(2*delta_x)*(func.f(u_approx[j+1])- func.f(u_approx[j]))\
+ delta_t*func.g(u_approx, delta_x, j)\
+ delta_t*func.s(time, position, u_approx, j))/2