Validation

Every solver in the engine ships with tests that run in CI on every change. Three kinds:

1. Exact solutions. Start from a closed-form soliton, run for many periods, compare pointwise.
2. Invariants. Compute the conserved quantities before and after and demand they agree to round-off.
3. Qualitative physics. Two solitons must emerge from a collision with their original amplitudes.

Mechanics

Scenario	Checked	Result
Projectile	position against the closed form at any time step	round-off
Mass on a spring	period against Verlet’s known dispersion, energy drift	1e-8, 1e-5
Atwood machine, block and hanging mass	acceleration, tension, normal force	round-off
Simple pendulum, 2 rad	period against the elliptic integral, convergence order	1.7e-8, order 2.0
Block on incline	at rest with friction $m g \sin\theta$; sliding acceleration	1e-10
Sliding block	stopping distance, friction work, ledger drift	4e-9, 5e-10, 3e-9
Collisions	elastic and inelastic outgoing velocities, energy lost, 90° scattering of equal discs	1e-10
Rolling disc	rolling acceleration and $v = \omega R$; slipping when $\mu_s$ is too small	1e-8
Seesaw	balanced stays still; tipping angular acceleration	1e-9
Bouncing ball	apex ratios $e^2$, first landing time	3e-5, 1e-6 s
Massive pulley, flywheel	acceleration, both tensions, rim speed	1e-8
Every catalogue scenario	builds, runs, round-trips through JSON	passes

Waves

Equation	Test	Error
KdV	single soliton, $t = 5$	$5 \times 10^{-8}$
KdV	two-soliton invariants, 8000 steps	drift $< 10^{-8}$
KdV	collision amplitude recovery	within $0.02$ of exact
NLS	moving bright soliton, $t = 10$	$3 \times 10^{-9}$
NLS	two-soliton invariants, 10000 steps	drift $< 10^{-8}$

Reproduce with:

git clone https://github.com/soliton-physics/soliton
cd soliton && cargo test --release

The playground shows the invariants and their drift live in the side panel, so you can watch the solver’s accuracy while it runs.