def _get_order_and_exponentiation_step(method):
    """Return order and exponentiation step given ``method``.

    Given ``method`` we return the initial order of the approximation error of the
    sequence under consideration (order) as well as the step size representing the
    growth of the exponent in the series expansion of the limit (exponentiation_step).
    See function ``richardson_extrapolation`` for more details.

    For different methods, different values of order and exponentiation step apply.
    Consider the following examples, where we continue the notation from function
    ``richardson_extrapolation`` and use O() to denote the Big O Laundau symbol.

    Central Differences.
        Derivative approximation via central difference is given by
            g(h) := [f(x + h) - f(x - h)] / 2h = f'(x) + r(x, h),
        where r(x, h) denotes the remainder term.

        If we expand the remainder term r(x, h) we get
            r(x, h) = a0*(h**2) + a1*(h**4) + a2*(h**6) + ...
        with a0 = f''(x) / 2!, a1 = f'''(x) / 3! etc.

        Rearanging terms we can write L := f'(x) = g(h) - r(x, h) = g(h) + O(h**2) and
        we notice that order = 2 and exponentiation_step = 2.

    Forward Differences.
        Derivative approximation via forward difference is given by
            g(h) := [f(x + h) - f(x)] / h = f'(x) + r(x, h),
            where again r(x, h) denotes the remainder term.

        If we expand the remainder term r(x, h) we get
            r(x, h) = a0*(h**1) + a1*(h**2) + a2*(h**3) + ...
        with a0 = f''(x) / 2!, a1 = f'''(x) / 3! etc.

        Rearanging terms we can write L := f'(x) = g(h) - r(x, h) = g(h) + O(h) and
        we notice that order = 1 and exponentiation_step = 1.

    Backward Differences.
        Analogous to forward differences.


    Args:
        method (str): One of ["central", "forward", "backward"], default "central".

    Returns:
        order (int): Initial order of the approximation error of sequence elements.

        exponentiation_step (int): Step representing the growth of the exponent in the
            series expansions of the limit.

    Example:
    >>> _get_order_and_exponentiation_step('central')
    (2, 2)

    """
    lookup = {
        "central": (2, 2),
        "forward": (1, 1),
        "backward": (1, 1),
    }

    order, exponentiation_step = lookup[method]
    return order, exponentiation_step