FA-87042 / Physics integrator stability / Member archive

Adaptive integrator propagates the low-order Euler solution · case 02

The error estimate refers to Heun but the state follows Euler, so accuracy is worse than tol suggests.

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 1	`[0.004414, 157, 3, 0.013378]`	`[0.003263, 158, 3, 0.025334]`	Failed

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