def _construct_approximation(self, basis_kwargs, coefs_list):
        """
        Construct a collection of derivatives and functions that approximate
        the solution to the boundary value problem.

        Parameters
        ----------
        basis_kwargs : dict(str: )
        coefs_list : list(numpy.ndarray)

        Returns
        -------
        basis_derivs : list(function)
        basis_funcs : list(function)

        """
        derivs = self._construct_derivatives(coefs_list, **basis_kwargs)
        funcs = self._construct_functions(coefs_list, **basis_kwargs)
        return derivs, funcs