Measures CPU performance by solving the stiff Van der Pol ODE with a 4th-order Runge-Kutta method over 1 million steps. RK4 performs 4 force evaluations per step — 4× the arithmetic of a plain Euler solver. Lower time is better.
The Van der Pol oscillator, named after Balthasar van der Pol who studied it in the 1920s while analyzing vacuum-tube circuits, is a canonical nonlinear oscillator with a self-sustaining limit cycle. Unlike a simple harmonic oscillator, it exhibits nonlinear damping: for small amplitudes the damping is negative (energy is added), and for large amplitudes it is positive (energy is dissipated). This drives trajectories toward a stable oscillating state regardless of initial conditions.
The equation x'' − μ·(1−x²)·x' + x = 0 becomes stiff for large μ — the solution alternates between slow drift phases and rapid spike-like transitions that require small timesteps to capture accurately. A plain Euler solver would need an impractically tiny dt to remain stable, which is why this benchmark uses the 4th-order Runge-Kutta method (RK4). RK4 evaluates the right-hand side four times per step with a weighted average, achieving 4th-order accuracy and tolerating much larger timesteps.
The benchmark runs 1 000 000 RK4 steps with μ = 5, x₀ = 2, v₀ = 0, dt = 0.01. Each step performs four right-hand side evaluations involving roughly ten floating-point operations each, for approximately 40 million operations total. The tight loop with no memory traffic beyond a handful of registers tests the CPU's ability to sustain throughput in dependent floating-point chains. This makes it a more demanding benchmark than the single-Euler-step variants, penalizing processors with poor pipeline depth or branch-prediction under data-dependent conditions.