1. Modified Nodal Analysis (MNA) & Trapezoidal Companion Models
Every animation frame runs 16 numerical substeps solving [G]{x} = {z} via partial-pivoting Gaussian elimination. Capacitors and inductors are discretized with 2nd-order A-stable Trapezoidal integration, while wires automatically split at mid-segment T-junctions to measure exact branch currents.
2. Berkeley SPICE3 pnjlim Newton-Raphson Semiconductor Convergence
Nonlinear PN junctions (Silicon diodes, multi-bandgap LEDs, reverse-breakdown Zeners, and 3-terminal Ebers-Moll BJT transistors) iterate to sub-microvolt convergence using logarithmic voltage-step damping so exponential Shockley currents never overflow.
3. 4th-Order Runge-Kutta (RK4) Physics & Ray Optics
Classical mechanics experiments integrate coupled nonlinear differential equations (including the full Euler-Lagrange chaotic double pendulum and quadratic aerodynamic drag) with <0.001% energy drift.