Fix ARKODE reinit

[ChrisRackauckas]

Needs a test case

[superckl]

I can verify this fixes the error, but callbacks with ARKODE still seem to be behaving weird. Take this test case (which resulted in a runtime error previously):

using Sundials, DiffEqBase, Test

tspan = [0, 200]
E = 1E-2
h0 = 1

fun = ODEFunction((dh, _, _, _) -> dh .= -E, jac = (J, _, _, _) -> J .= 0)
prob = ODEProblem(fun, [h0], tspan)

cb = ContinuousCallback((h, _, _) -> h[1], terminate!)

sol_ark = solve(prob, ARKODE(), callback = cb)
sol_bdf = solve(prob, CVODE_BDF(), callback = cb)

@test isapprox(sol_bdf.t[end], 1/E, rtol = 1E-3)
@test isapprox(sol_bdf[end][1], 0, atol = 1E-3)
@test isapprox(sol_ark.t[end], 1/E, rtol = 1E-3)
@test isapprox(sol_ark[end][1], 0, atol = 1E-3)

which outputs

Test Failed at i:\My Drive\Research\Code\julia solver\Sundials\test\arkode_callback.jl:17
  Expression: isapprox(sol_ark.t[end], 1 / E, rtol = 0.001)
   Evaluated: isapprox(0.0, 100.0; rtol = 0.001)
ERROR: There was an error during testing

The system should be integrated to 1/E=1E2 and then stop because h=0. With CVODE_BDF, all is fine, but ARKODE seems to exit at t=0. Without the callback, ARKODE integrates the system fine:

display(solve(prob, ARKODE()))

retcode: Success
Interpolation: 3rd order Hermite
t: 6-element Vector{Float64}:
   0.0
   0.004112271831573867
   0.3427118254794238
   5.90547982484689
 117.16083981219622
 200.0
u: 6-element Vector{Vector{Float64}}:
 [1.0]
 [0.9999588772816843]
 [0.9965728817452059]
 [0.9409452017515313]
 [-0.17160839812196294]
 [-1.000000000000002]

[ChrisRackauckas]

Can you see what happens if you swap fun 1 and 2 in the overload? I think I did it right: we have implicit-explicit and they have explicit-implicit. But double check.

[superckl]

Switching the functions seems to have no effect. This seems like it might be unrelated to this PR, I can just discover it now -- perhaps I should open a separate issue?

[ChrisRackauckas]

Alright, well this is at least right so let's merge this and open an issue to investigate next steps.

[HumHongeKamyaab]

Mentioning this discourse thread here https://discourse.julialang.org/t/facing-problems-with-sundials-jl-arkode-with-discrete-callback/119278?u=humhongekamyaab
as it is related with reinit of ARKODE