set_u! not respected on first time step of Euler()

[mjowen]

Describe the bug 🐞

set_u! does not work when applied to the first time step. It does update the values of u in the integrator but the derivative is not reevaluated on the new state. This looks to only apply for the Euler() algorithm.

Expected behavior

set_u! should mark the derivative as having changed, so the first step should lead to an increase in u[1] since u[2] is positive.

Minimal Reproducible Example 👇

using DifferentialEquations
function f!(du, u, p, t)
    x, y = u
    du[1] = y
    du[2] = 0
end

prob1 = ODEProblem(f!, [4.0,-1.0], (0.0,1.0))

int = init(prob1, Euler(); dt=0.002, adaptive=false, save_everystep=false)
println("Failing version: Change u[2] to 2 before the first step")
@show (int.t,int.u)
println("Change u[2] here")
set_u!(int, [4.0, 2.0])
@show (int.t,int.u)
step!(int)
@show (int.t,int.u)
println("u[1] decreased but should have increased")
step!(int)
@show (int.t,int.u)
println("Later steps work fine")
println()

int = init(prob1, Euler(); dt=0.002, adaptive=false, save_everystep=false)
println("Working version: Change u[2] to 2 after the first step")
@show (int.t,int.u)
step!(int)
@show (int.t,int.u)
println("Change u[2] here")
set_u!(int, [4.0, 2.0])
@show (int.t,int.u)
println("This time u[1] didn't decrease because we only used set_u! after the first step")
step!(int)
@show (int.t,int.u)
step!(int)
@show (int.t,int.u)

Error & Stacktrace ⚠️
Output from MRE.

Failing version: Change u[2] to 2 before the first step
(int.t, int.u) = (0.0, [4.0, -1.0])
Change u[2] here
(int.t, int.u) = (0.0, [4.0, 2.0])
(int.t, int.u) = (0.002, [3.998, 2.0])
u[1] decreased but should have increased
(int.t, int.u) = (0.004, [4.002, 2.0])
Later steps work fine

Working version: Change u[2] to 2 after the first step
(int.t, int.u) = (0.0, [4.0, -1.0])
(int.t, int.u) = (0.002, [3.998, -1.0])
Change u[2] here
(int.t, int.u) = (0.002, [4.0, 2.0])
This time u[1] didn't decrease because we only used set_u! after the first step
(int.t, int.u) = (0.004, [4.004, 2.0])
(int.t, int.u) = (0.006, [4.007999999999999, 2.0])
(0.006, [4.007999999999999, 2.0])

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `/private/var/folders/sq/qg5k_lb90mvgph1ysj0cz4sh0000gp/T/jl_wbGNxW/Project.toml`
  [0c46a032] DifferentialEquations v7.16.1

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

Status `/private/var/folders/sq/qg5k_lb90mvgph1ysj0cz4sh0000gp/T/jl_wbGNxW/Manifest.toml`
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• Output of versioninfo()

Julia Version 1.11.5
Commit 760b2e5b739 (2025-04-14 06:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin24.0.0)
  CPU: 14 × Apple M4 Pro
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  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m1)
Threads: 1 default, 0 interactive, 1 GC (on 10 virtual cores)
Environment:
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  JULIA_VSCODE_REPL = 1