import { Equation, Step } from './types.js';
/**
 * Represents a system of differential equations.
 */
export declare class DifferentialSystem {
    private readonly dimensions;
    /**
     * Represents the actual differential equations within the system
     */
    private readonly equations;
    /**
     * Initialize a new system of differential equations.
     * @param dimensions The number of equations in this system
     * @example
     * const system = new DifferentialSystem(3); // x, y, z
     */
    constructor(dimensions: number);
    /**
     * Set a differential equation for a specific dimension. All differential equations must be set before solving.
     * @param dimension The 0-indexed dimension number to set the equation for
     * @param de The differential equation for this dimension must accept a global state vector ordered by dimension and derivative order
     * ```
     * x, dx/dt, ..., d(i-1)x/dt(i-1),
     * y, dy/dt, ..., d(j-1)y/dt(j-1),
     * z, dz/dt, ..., d(k-1)z/dt(k-1),
     * ... (higher dimensions)
     * ```
     * Where `i` is the highest order of `x` (dimension 0), `j` is the highest order of `y` (dimension 1) and `k` is the highest order of `z` (dimension 2)
     * @param ic Initial conditions for this dimension, ordered `x`, `dx/dt`, ..., `d(n-1)x/dt(n-1)`
     * @example
     * const sigma = 1;
     * const rho = 1;
     * const beta = 8 / 3;
     * const dx = (t, x, y, z) => sigma * (y - x);
     * const dy = (t, x, y, z) => x * (rho - z) - y;
     * const dz = (t, x, y, z) => x * y - beta * z;
     * system.setEquationFor(0, dx, 10); // x0 = 10
     * system.setEquationFor(1, dy, 10); // y0 = 10
     * system.setEquationFor(2, dz, 10); // z0 = 10
     */
    setEquationFor(dimension: number, de: Equation, ...ic: number[]): void;
    /**
     * Solve this system of differential equations from `t=0` to `t=tf` with timestep `dt`.
     * @param dt The timestep
     * @param tf The final time
     * @returns Square array with the first index being the 0-indexed dimension and second index being the time index, each entry contains the timestamp and all orders of derivatives
     * @example
     * const data = system.solve(1e-3, 4);
     */
    solve(dt: number, tf: number): Step[][];
}