import { Equation, Step } from './types';
/**
 * Represents a one dimensional time-dependent differential equation.
 */
export declare class DifferentialEquation {
    /**
     * Contains methods and data for the actual differential equation
     */
    private readonly DE;
    /**
     * Initialize a new one-dimensional differential equation.
     * @param dnx Equation for `d(n)x/dt(n)` as a function of `t`, `x`, `dx/dt`, ..., `d(n-1)x/dt(n-1)`
     * @param x0 Initial conditions ordered by `x`, `dx/dt`, ..., `d(n-1)x/dt(n-1)`
     * @example
     * // y = e^x can be represented by dx/dt = x, at time t=0, x=1
     * const exp = new DifferentialEquation((t, x) => x, 1);
     */
    constructor(dnx: Equation, ...x0: number[]);
    /**
     * Solve this differential equation from `t=0` to `t=tf` with timestep `dt`.
     * @param dt The timestep
     * @param tf The final time
     * @returns An array containing each timestep and all orders of derivatives
     * @example
     * const data = exp.solve(1e-3, 4);
     */
    solve(dt: number, tf: number): Step[];
}