some ode45 features

[JeffBezanson]

ode45 should support stepping from high to low like ode23 does, and both should also support any-size vectors of steps instead of just [t0, tfinal].

I'd like to do

function tracywidom()
    t0 = 5.
    tn = -8.
    dx = .005

    deq = function (t::Float64, y::Vector{Float64})
        [y[2]; t*y[1]+2*y[1]^3; y[4]; y[1]^2]
    end

    y0 = [airy(t0); airy(1,t0); 0; airy(t0)^2]

    (t, y) = ode45(deq, [t0:-dx:tn], y0)

    F2 = exp(-y[:,3][:])
    f2 = gradient(F2,t)
    return (t, f2)
end

[ViralBShah]

ode23 derives from Cleve's NCM, whereas ode45 is from octave - which is why the different styles and interfaces.

I presume you also want to include plots in this if you were playing around with things...

[vtjnash]

see also #75. sounds like a general framework for ODE solvers would be useful to create, then this can all be moved to a package for individual authors to provide specialized solutions.

i suspect it might require keyword arguments (or the approach in the new sort interface?)

[ViralBShah]

We need someone to spearhead our ODE effort. I might just be able to do some basic stuff, once we are through the ubuntu release stuff.

[ViralBShah]

@tshort Now that we have Sundials.jl, should we get rid of all the various half-baked ODE functions in ODE.jl? Perhaps ODE.jl should just be a high-level interface to Sundials.jl.

[pao]

I don't know about all, but probably the half-baked ones. I'd still like to see pure-Julia integrators, and there's some encouraging stuff being talked about on the mailing lists for automatically generating Jacobians etc. that would be good to take advantage of.

[ViralBShah]

I agree. I am tempted to close this one as wontfix, unless there is any objection.

[vtjnash]

just move to the ODE package I'm now hosting and close this one

[ViralBShah]

This issue is moved to ODE.jl.