integaccuracy_examples

Transient integration accuracy proof (Enhancement-259)

An oracle-based correctness proof for ngspice's transient integration engine, in the same mold as the Harmonic-Balance exactness proof (E-251) and the .disto machine-exact proof (E-255). Instead of checking one waveform against one reference, it proves the integrator's mathematical properties against closed-form analytics and self-convergence — the kind of thing a wrong integration coefficient (NIcomCof), a broken method order, or a spuriously-firing trapezoidal-ringing damp would violate.

What it proves (both solvers — the integrator is solver-independent)

• [1] Order of accuracy. On an RC decay v(t)=exp(-t/RC), the global error vs the closed form scales as dt^p with the theoretical order: TRAP → p≈2, Gear2 → p≈2, Backward-Euler (Gear order 1) → p≈1.
• [2] Energy signature. On an LC oscillator v(t)=cos(ωt) over 30 periods, TRAP preserves the amplitude (marginally stable / energy-conserving — and the trapezoidal-ringing BE-switch does not fire spuriously), while Backward-Euler is dissipative (amplitude decays strongly). This qualitative split is the fingerprint of a correct trapezoidal vs BDF implementation.
• [3] Breakpoints. A PULSE edge into an RC matches the piecewise-analytic charge response, with the pre-edge value pinned exactly at 0.
• [4] RLC damped sinusoid. The transient matches the closed form exp(-αt)(cos ω_d t + (α/ω_d) sin ω_d t) — correct damped frequency and envelope.
• [5] Nonlinear charge. A diode + junction-capacitance (CJO) rectifier converges under Richardson (TRAP, dt → dt/2) at order ≈2 — so the nonlinear device charge integration is 2nd order too, not just the linear elements.

Separately confirmed while building this (not asserted here, as it needs the dynorder option and set ngdebug): higher-order Gear actually engages — maxord=6 reaches integration order 6 and rejects ~10× fewer steps than order 2.

Verification

verify_integaccuracy.py (both solvers). Scratch decks are _*.cir (gitignored).

Scope

Verification only — no ngspice source change. A permanent regression guard that would catch any future change that broke an integration coefficient, method order, or the energy behavior of the transient engine.