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