"""
SciPy-based backend for solving boundary value problems
"""

from typing import Any, List, Dict
from ..api import BC


class ScipyBVPBackend:
    """
    Backend for solving boundary value problems using SciPy's solve_bvp.

    This backend will handle two-point boundary value problems where
    conditions are specified at multiple points in the domain.
    """

    def solve(
        self, system: Any, bvp: List[BC], tspan: tuple, options: Dict = None
    ) -> Any:
        """
        Solve a boundary value problem.

        Args:
            system: First-order system representation
            bvp: List of boundary conditions
            tspan: Integration domain (start, end)
            options: Additional solver options

        Returns:
            Solution object for BVP

        Raises:
            NotImplementedError: BVP implementation arrives in Milestone 5
        """
        raise NotImplementedError("BVP in Milestone 5")


def solve_bvp_scipy(equation, boundary_conditions, tspan, **kwargs):
    """
    Solve a BVP using SciPy's solve_bvp.

    This is a placeholder for future implementation.
    """
    raise NotImplementedError(
        "SciPy BVP backend will be implemented in later playbooks"
    )
