MCM/A题/数值分析检验/Prompt/6.md

TASK: Run convergence/robustness checks for baseline scenario.

INPUT DATA:

• Same configuration as Prompt 5, but run two numerics: A) dt = 1.0 s B) dt = 0.5 s
• Use identical params and scenario.

METHODOLOGY: For each z0:

1. Simulate with dt and dt/2 until termination.
2. Compare z(t) by resampling dt/2 solution at dt grid (take every 2nd sample).
3. Compute: z_diff_inf = max_k |z_dt[k] - z_dt2[2k]| tte_rel_err = |TTE_dt - TTE_dt2| / TTE_dt2
4. Event-location robustness: For each run, report the last two bracketing samples for the triggering event and the interpolated t*.

DELIVERABLES: A) “STEP_HALVING_TABLE_v1” CSV: z0, z_diff_inf, tte_rel_err, pass_bool B) “EVENT_BRACKET_REPORT_v1” JSON: for each z0: {reason, (t_k-1, g_k-1), (t_k, g_k), t_star} C) Single line verdict: "ROBUSTNESS_PASS" or "ROBUSTNESS_FAIL"

VALIDATION (hard thresholds):

• z_diff_inf < 1e-4
• tte_rel_err < 0.01 All z0 must pass or verdict is FAIL.

OUTPUT FORMAT: CSV, then JSON, then verdict line. No prose.