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VectorOfArray with adaptive time steps in OrdinaryDiffEq  #243

@aluque

Description

@aluque

Perhaps I am doing something wrong but combining VectorOfArray with adaptive stepsize control in OrdinarryDiffEq doesn't seem to work:

using OrdinaryDiffEq
using RecursiveArrayTools

u0 = VectorOfArray([ones(4, 4) for _ in 1:4])

# With this, error control works and the time steps are shorter:
# u0 = ones(4, 4, 4)

function dudt!(du, u, p, t)
    @. du = -u
end

tspan = (0.0, 100.0)
prob = ODEProblem(dudt!, u0, tspan)
integrator = init(prob, Midpoint(), dtmax=10.0)

for i in 1:10
    step!(integrator)
    @info "" integrator.EEst integrator.dt (integrator.cache.fsalfirst[1] === integrator.cache.k[1])
end            

println("Final time t = $(integrator.t)")
println("Solution u = $(integrator.sol.u[end][1, 1, 1])")
println("Exact u = $(exp(-integrator.t))")

This chooses the maximum allowed dt=10.0 and produces an inaccurate integration. To me its seems related to the use of recursivecopy! in apply_step! of OrdinaryDiffEq. It copies references to the underlying arrays instead of contents.
After that the error estimates are zero.

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