Instability of Shooting Method

Using shooting, accuracy is not symmetric at boundary points

Demo not replicable on my machine

plt = plot(xaxis = L"x", yaxis = ([-1.2, 0.5], L"u(x)"),
           title = "Shooting instability", leg=:topleft);

for lambda in 6:4:18
  g1(u,du) = u+1
  g2(u,du) = u
  phi = (x, u, du_dx) -> lambda^2*(u + 1) #lambda^2 (u+1)
  x,u = FNC.shoot(phi, (0.0, 1.0), g1, g2, [-1, 0])
  plot!(x, u, label = "lambda = $lambda")
end

plt