FA-87052 / Physics integrator stability / Member archive

Adaptive steps overshoot the requested end time · case 02

The solution is reported for a time later than t_end.

Member previewVariant 2 · 3 implementations · 8 checks per implementation

Case contract

solve(y0, lam, s, t_end, dt0, tol): integrate y'=-lam*y+s to t_end with the embedded Euler/Heun pair. err=|y_heun-y_euler|/max(1,|y|) at the step start. Accept if err<=tol (propagate Heun); grow h by min(2, 0.9*(tol/err)^(1/2)) (2 when err=0); on reject shrink by max(0.2, 0.9*(tol/err)^(1/2)). Steps are clipped to t_end; at most 500 attempts. Return [y, accepted, rejected, last h] rounded.

Why this case matters

Game and robotics physics loops depend on integrator update order, step control and stabilization terms; a wrong decision point turns a stable simulation into drifting or exploding motion.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
case 0	`[0.415244, 23, 1, 0.108119]`	`[0.386621, 23, 1, 0.024826]`	Failed

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