elif i == 0 and j == 1:
return 1
elif i == 1 and j == 0:
return 0
elif i == 1 and j == 1:
return 1
raise ValueError("Wrong i, j (i=%d, j=%d)." % (i, j))
d.define_ode(F, DFDY)
d.assign_dofs()
Y = zeros(d.ndofs)
J = d.assemble_J(Y)
error = 1e10
i = 0
while error > 1e-10:
F = d.assemble_F(Y)
dY = d.solve(J, F)
error = d.calculate_error_l2_norm(dY)
print "it=%d, l2_norm=%e" % (i, error)
Y += dY
i += 1
x = Y
from pylab import plot, legend, show
sln1, sln2 = d.linearize(x, 5)
x1, y1 = sln1
x2, y2 = sln2
plot(x1, y1, label="$u_1$")
plot(x2, y2, label="$u_2$")
legend()
show()
raise ValueError("Wrong i, j (i=%d, j=%d)." % (i, j))
# assign both F and J to the discrete problem:
d.define_ode(F, DFDY)
# enumeration of unknowns:
d.assign_dofs()
# definition of the initial condition for the global Newton method:
Y = d.get_initial_condition_euler()
#plot_Y(Y, a, b)
#stop
#Y = zeros((d.ndofs,))
# Newton's iteration:
error = 1e10
i = 0
J = d.assemble_J(Y)
while error > 1e-5:
F = d.assemble_F(Y)
dY = d.solve(J, F)
Y += dY
#plot_Y(Y, a, b)
error_dY = d.calculate_error_l2_norm(dY)
error_F = d.calculate_error_l2_norm(d.assemble_F(Y))
print "it=%d, l2_norm_dY=%e, l2_norm_F=%e" % (i, error_dY, error_F)
error = max(error_dY, error_F)
i += 1
plot_Y(Y, a, b)
