FA-87064 / Physics integrator stability / Member archive

Exact steps never grow the step size · case 04

A constant-slope phase keeps the tiny initial step forever and wastes work.

Member previewVariant 4 · 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	`[-2.779, 1, 0, 0.5]`	`[-2.779, 1, 0, 1.0]`	Failed

MEMBER ARCHIVE

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