Does a While Iterator subsystem prevent ode1be implicit iterations? Backward Euler becomes explicit in my custom DAE solver

Hi all,

I’m trying to solve a DAE in Simulink using a custom Newton–Raphson (NR) loop implemented with a While Iterator Subsystem.

What I’m doing

• The overall problem is a DAE where I solve algebraic unknowns using NR at every time step.
• Inside the While Iterator Subsystem, I compute the residual and (as part of that) compute the ODE part’s state derivative dx/dt.
• The Integrator block is outside the While Iterator Subsystem (continuous Integrator), so time advances only once per major step.
• The Integrator’s current state x(t) is fed into the While Iterator as the initial guess for the residual evaluation, and the computed dx/dt is fed back to the Integrator input.
• The solver is set to fixed-step with ode1be (Backward Euler) (step size: [1e-3]).

Conceptually:

1. Integrator outputs x_k
2. While Iterator runs NR iterations using x_k (and other signals) to solve algebraic variables and compute f(...) = dx/dt
3. Integrator updates the state using ode1be

Expected behavior

With ode1be, I expect an implicit update (Backward Euler):

meaning Simulink should effectively evaluate the derivative using the “future” state (or iterate internally to satisfy the implicit equation).

Observed behavior

When the derivative dx/dt is produced through my While Iterator + NR loop structure, the result matches Forward Euler:

However, if I remove the While Iterator / custom NR loop and compute dx/dt in a normal continuous path, ode1be behaves correctly (implicit/backward).

So it looks like my model structure causes ode1be to lose its implicit behavior and behave like an explicit integrator.

• schimetics for custom DAE Sovler

Questions

1. Why does ode1be effectively become forward/explicit when the derivative is computed inside a While Iterator subsystem?

• Does While Iterator prevent the solver from performing implicit iterations / re-evaluations of the derivative with tentative x_{k+1}?
• Is the While Iterator subsystem treated as “non-reentrant” or “discrete-like” in a way that breaks the implicit loop needed for ode1be?

2. Is there a recommended way to structure a custom DAE + NR loop while still using an implicit integrator like ode1be?

• I specifically want to avoid using the Algebraic Constraint block.

3. Are there alternative Simulink-native DAE approaches (without Algebraic Constraint) that can keep the stability benefits of implicit integration?

For example: using a different solver class (ode15s/ode23t), using an S-Function, using a discrete update with manual backward Euler inside NR, etc.

If needed, I can share a minimal reproducible example model.

ps. I used AI for translation

Thanks!