[julia-users] Backwards Euler method for differential equations

[João Paquim]

Hey everyone,

I'm learning this language, and doing a couple of simple examples to see if 
I understand everything.

I want to solve the first order differential equation u' = f(u, t), with 
initial condition u(0) = ui. Discretizing u' as (u(t) - u(t-dt)) / dt, and 
rearranging, means I have to solve the equation:
u(t) - u(t-dt) - dt * f(u, t). To solve the equation, I'm calling the 
function fzero.

Can anyone please comment on this implementation? Maybe post some 
pathological case where it wouldn't work?

using Roots
function beuler(f, dt, ti, tf, ui)
    N=int((tf-ti)/dt)+1
    t=ti:dt:tf
    u=zeros(N)
    u[1]=ui
    for i=2:N
        u[i]=fzero(u1->u1-u[i-1]-dt*f(u1, t[i]), u[i-1])
    end
    return t, u
end

Cheers,
João Paquim