Numerical methods and inspectable histories

The shared integrator returns time [s], a (samples, states) history array, method name and derivative evaluation count. Every sampled state is inspectable. Euler and RK4 use the caller’s time grid; adaptive methods use SciPy solve_ivp with separate internal steps and interpolate onto that grid.

import numpy as np
from engineeringkit.integrators import integrate_ode
result = integrate_ode(lambda t, y: -y, [1.], np.linspace(0, 2, 101), "rk4")
print(result.summary())
fig, ax = result.plot(["normalized state"])

Euler has first-order global accuracy; classical RK4 has fourth-order global accuracy for sufficiently smooth problems. Neither is unconditionally stable. For decay y’=-a*y, Euler requires 0<a*dt<2 for stability. Prefer Radau or BDF for stiff problems. Numerical tolerances control local error, not a proof of physical fidelity. The tests check decay against exp(-t), RK4 convergence, undamped oscillator energy, and critically damped response.

SI policy

Plain numbers have no dimensional metadata. Callers must supply SI values and use the units conversion helpers explicitly. Labels on plots should include physical units. EngineeringKit does not automatically detect dimensional mistakes.

Regression behavior

PID with ki=0 omits the integrator, preventing a spurious pole at zero. Routh stability excludes imaginary-axis roots and handles auxiliary zero rows. Root locus requires a strictly proper open-loop model and does not track branch ordering between gains. ADC quantization uses 2**bits mid-rise reconstruction levels, with saturation at the first and last bin centers. Fin efficiency at zero m*L is its analytic limit, one.