tangent/ode

ODE integration for JavaScript (ESM). Browser-first, runs in Node.js and Deno. The differential-equations leaf of the tangent suite — MIT-licensed.

• rk45 — adaptive Dormand-Prince (scipy's RK45 / MATLAB's ode45): 5th order with embedded error control, 4th-order dense output, and bracketed event detection
• rosenbrock — adaptive, A-stable solver for stiff systems (reaction kinetics, diffusion, fast-slow dynamics), built on lina for the linear solves
• euler / rk2 / rk4 — classic fixed-step integrators
• solve — one entry point dispatching by method name

Systems are y' = f(t, y) with plain array (or scalar) state — no matrix types to learn.

Install

npm install @tangent.to/ode     # npm
deno add jsr:@tangent/ode       # Deno / JSR

Usage

import { rk45, solve } from '@tangent.to/ode';

// Lotka-Volterra predator-prey
const [a, b, c, d] = [1.5, 1, 3, 1];
const sol = rk45(
  (t, [x, y]) => [a * x - b * x * y, -c * y + d * x * y],
  [0, 15], [10, 5],
  { tEval: Array.from({ length: 151 }, (_, i) => i * 0.1) },
);
sol.t;        // time points
sol.y[0];     // prey trajectory (component-major, like scipy's .y)
sol.y[1];     // predator trajectory

// Stiff system -> switch method, same interface
solve(robertsonKinetics, [0, 1e4], [1, 0, 0], { method: 'rosenbrock' });

Events

// Find every time the pendulum passes through vertical
const sol = rk45(pendulum, [0, 20], [Math.PI / 2, 0], {
  events: (t, [theta]) => theta,   // roots of g mark events
});
sol.events[0].t;   // event times, located by bisection on the interpolant

PDEs by the method of lines

There is no PDE solver — the browser-scale answer is to discretize space yourself and integrate the resulting ODE system. examples/advection-diffusion.mjs solves 1-D solute transport (dc/dt = D c_xx - v c_x) on a 101-node grid this way, handing the stiff system to rosenbrock.

Validation against scipy

tests_compare-to-scipy/ integrates shared problems with both tangent/ode and scipy.integrate.solve_ivp, sampled at identical time points: non-stiff cases (exp, decay, oscillator, Lotka-Volterra) against scipy's RK45, stiff cases (Van der Pol mu=100, Robertson kinetics) against scipy's Radau. Requires uv and Node:

npm run test:scipy

Scope

Explicit non-stiff and Rosenbrock stiff integration for first-order systems, double precision, sized for the suite's modeling workloads (systems dynamics, transport, kinetics, ecology). Out of scope for now: implicit multistep (BDF) beyond Rosenbrock, DAEs, boundary-value problems, symplectic integrators.

License

MIT.