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Phase Portraits & Numerical Integration

Interactive 3D simulation of phase portraits for differential equations: a direction-field grid, a swarm of trajectories, and side-by-side Euler vs Runge-Kutta probes that reveal how step size and integration method affect numerical accuracy.

Mathematics3DModerate60 FPS

Differential equations rarely have tidy closed-form solutions, so most real work solving them happens numerically. This simulation lays out the phase plane of a chosen system as a 3D direction field, flows a swarm of trajectories through it, and races two probes from the same starting point — one stepped with forward Euler, one with 4th-order Runge-Kutta — so you can see exactly how step size and method choice affect how faithfully a numerical solution tracks the true flow.

⚙ Under the hood

Interactive 3D phase-plane simulation of differential equations: a direction-field grid, a swarm of numerically integrated trajectories, and side-by-side Euler vs Runge-Kutta probes that reveal how step size and integration method affect accuracy.

Three.jsdifferential equationsnumerical methodsEuler methodRunge-Kuttamath

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install