FA-87009 / Physics integrator stability / Member archive

RK4 third stage reuses the first-stage slope · case 04

The method degrades to second order and energy error grows with dt^2.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

solve(x0, v0, k, c, F, wf, dt, steps): unit mass x''=-k*x-c*v+F*cos(wf*t) with wf in rad/s, t starting at 0, integrated with classical RK4. Return [x, v, t] rounded to 6.

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	`[-0.240565, -1.356846, 1.2]`	`[-0.164785, -1.352613, 1.2]`	Failed

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This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

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