{"slug":"numerical-stability","source_name":"numerical-stability","name":"Numerical Stability","description":"Analyze and enforce numerical stability for time-dependent PDE simulations. Use when selecting time steps, choosing explicit/implicit schemes, diagnosing numerical blow-up, checking CFL/Fourier criteria, von Neumann analysis, matrix conditioning, or detecting stiffness in advection/diffusion/reaction problems.","version":1,"lift":{"pass_rate_delta_pts":36.36,"pass_rate_pct":36.4,"total_cases":22,"passed_cases":8,"tokens_delta_pct":56.9,"turns_delta_pct":0,"verdict":"mixed","benchmark_model":"gemini-3.6-flash","grading_method":"judged","completed_at":"2026-07-26T11:54:33.391007+00:00"},"skill_score":0.3636,"benchmark_models":[{"model":"gemini-3.6-flash","headline":true,"delta_pts":36.36,"with_pass_pct":36.4,"without_pass_pct":0,"tokens_delta_pct":56.9,"turns_delta_pct":0,"total_cases":22,"cases_aggregated":20,"verdict":"mixed","never_hurt":false,"completed_at":"2026-07-26T11:54:33.391007+00:00","run_id":"f736c4f4-95e5-43f8-af8f-1418faf52a98","version_number":1,"is_latest_version":true,"gate":null}],"trust":{"skill_safety":"passed","safety_status":"clean","intent_verdict":null,"content_status":"clean","indexable":true},"license":null,"install_count":0,"manifest_hash":"5269473d607187f0932c09d66237288ee1c844bae5fbd58f91bc4bdd98d8be8e","raw_url":"https://app.decimal.ai/s/numerical-stability/SKILL.md","scorecard_url":"https://app.decimal.ai/skills/numerical-stability"}