OpenCircuit Nonlinear Solver

A dependency-free numerical kernel for nonlinear circuit operating points. It combines damped Newton-Raphson iteration, analytic or numerical Jacobians, parameter continuation, step limiting, and a nonlinear modified-nodal-analysis bridge.

Capabilities

• Multi-variable damped Newton iteration.
• Analytic, central-difference, or forward-difference Jacobians.
• Backtracking line search with residual reduction.
• Maximum-step limiting for exponential semiconductor models.
• Absolute, relative, step, iteration, and pivot tolerances.
• Full convergence history and failure diagnostics.
• Sequential parameter continuation using the previous solution as the next initial guess.
• Nonlinear two-terminal device stamping into an MNA system.
• Analytic or numerically estimated device conductance.

Generic nonlinear solve

import { solveNonlinear } from '@opencircuitlabs/nonlinear-solver';

const result = solveNonlinear(
  ([x, y]) => [x*x + y*y - 1, x - y],
  [0.8, 0.6],
  { jacobian: ([x, y]) => [[2*x, 2*y], [1, -1]] }
);

Nonlinear MNA

import { solveNonlinearMNA } from '@opencircuitlabs/nonlinear-solver';

const result = solveNonlinearMNA({
  linearMatrix: [[1 / 1000]],
  rhs: [5 / 1000],
  devices: [{
    id: 'D1',
    positive: 0,
    negative: null,
    current: voltage => 1e-12 * Math.expm1(voltage / 0.02585),
    conductance: voltage => 1e-12 / 0.02585 * Math.exp(voltage / 0.02585)
  }],
  initialGuess: [0.6]
});

null or undefined terminals represent ground. Device current is positive from the positive terminal to the negative terminal.

Failure handling

Non-convergence, singular Jacobians, invalid model output, and line-search failure throw NonlinearSolverError. When iteration has begun, error.diagnostics contains the last solution, residual norm, iteration number, and convergence history.

Development

npm install
npm test
npm run example

License

MIT © 2026 OpenCircuitLabs