MIRK4 interpolation bug

Describe the bug 🐞

The interpolated solution from using the MIRK4 method to solve a BVProblem seems to be bugged. I can not access the derivatives of the solution like in the case of solutions to ODEProblems using the method given here: https://discourse.julialang.org/t/differentialequations-and-derivatives-of-solutions/49995/2. I just get the value of the solution at time t and not its derivative at time t.

Expected behavior

For a solution sol to a system of ODEs x'(t) = f(x(t)) with boundary conditions specified, get the derivatives of each component with respect to time using sol(t,Val{1})

Minimal Reproducible Example 👇

using DifferentialEquations

const g = 9.81
L = 1.0
tspan = (0.0, pi / 2)
function simplependulum!(du, u, p, t)
    θ = u[1]
    dθ = u[2]
    du[1] = dθ
    du[2] = -(g / L) * sin(θ)
end

function bc1!(residual, u, p, t)
    residual[1] = u[end ÷ 2][1] + pi / 2 # the solution at the middle of the time span should be -pi/2
    residual[2] = u[end][1] - pi / 2 # the solution at the end of the time span should be pi/2
end
bvp1 = BVProblem(simplependulum!, bc1!, [pi / 2, pi / 2], tspan)
ivp1! = ODEProblem(simplependulum!,[pi/4,0],tspan)
sol1 = solve(bvp1, MIRK4(), dt = 0.05)
sol2 = solve(ivp1!)

println(sol1(0.81))
println(sol1(0.81,Val{1}))

println(sol2(0.81))
println(sol2(0.81,Val{1}))

Error & Stacktrace ⚠️ No errors

Environment:

Output of using Pkg; Pkg.status()

`~/.julia/environments/v1.10/Project.toml`
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  [26cc04aa] FiniteDifferences v0.12.32
  [f6369f11] ForwardDiff v0.10.36
  [7073ff75] IJulia v1.25.0
  [de52edbc] Integrals v4.4.1
  [a98d9a8b] Interpolations v0.15.1
  [b964fa9f] LaTeXStrings v1.3.1
  [91a5bcdd] Plots v1.40.5
  [d330b81b] PyPlot v2.11.5
  [1fd47b50] QuadGK v2.9.4
  [e88e6eb3] Zygote v0.6.70

Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

`~/.julia/environments/v1.10/Manifest.toml`
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  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2

Output of versioninfo()

Julia Version 1.10.4
Commit 48d4fd48430 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 12 × AMD Ryzen 5 4600H with Radeon Graphics
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 1 default, 0 interactive, 1 GC (on 12 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS =

SciML / BoundaryValueDiffEq.jl

MIRK4 interpolation bug #197