ODE.jl - backwards (negative in time) integration

[Chris]

Hello,

I came across this issue (recreated here using example code):

julia> using ODE

julia> function f(t, y)

           # Extract the components of the y vector

           (x, v) = y

           # Our system of differential equations

           x_prime = v

           v_prime = -x

           # Return the derivatives as a vector

           [x_prime; v_prime]

       end;

julia> # Initial condtions -- x(0) and x'(0)

       const start = [0.0; 0.1]

WARNING: redefining constant start

2-element Array{Float64,1}:

 0.0

 0.1

julia> # Time vector going from 0 to 2*PI in 0.01 increments

       time = 0.:-.1:-4pi;

julia> t, y = ode45(f, start, time);

This hangs for a long time (I've waited up to a minute before killing it). Is this a bug, or something I'm doing wrong? I do notice that reversing the time vector (-4pi:.1:0.0) yields a result.

Thanks,

Chris

[Mauro]

This is a bug, could you file an issue? Thanks! Note that some solvers,
even some of the Runge-Kutta family work, for instance ode78, ode45_fe,
ode21 or ode23s.

[Chris]

Submitted https://github.com/JuliaLang/ODE.jl/issues/104 

Thanks.

[Chris Rackauckas]

Won't some of the Runge-Kutta solvers be really unstable with a small negative Delta t? What happens when you use a fixed time step method: does it run and diverge?

[Chris Rackauckas]

Nevermind, I realize that thought was silly because of how linear stability is defined. Carry on.

Though I would still give a fixed timestep method a try to narrow down the bug to adaptive stepping. There may be some issue somewhere, something weird like how it chooses min/max timesteps?