#pragma once

#include "vec.h"
#include "ivp.h"
#include <utility>

// Function declarations

// Given the boundary-value problem (BVP)
//     u"(x) = f( x, {u(x), u'(x)} )
// with the boundary conditions
//     u(a) = u
//             a
// and
//     u(b) = u ,
//             b
// find an approximation to the solution.
//
// Parameters:
//   f         The right-hand side of the ODE
//                 u" = f( x, {u, u'} )
//   x_range   A pair [a, b]
//   u_bndry   A pair [u , u ] such that u(a) = u     u(b) = u
//                      a   b                    a            b
//   eps_abs   The maximum error that the solution is away from u
//                                                               b
//   max_iterations
//             The maximum number of iterations allowed
//   h         The initial 'h' value for the IVP solver
//   h_range   A pair of [h   , h   ] that bound the allowable
//                         min   max
//             step sizes

ivp<vec<2>> bvp( vec<2> f( double x, vec<2> u ),
     std::pair<double, double> x_range,
     std::pair<double, double> u_bndry,
     double eps_abs,
     unsigned int max_iterations,
     double h,
     std::pair<double, double> h_range
);

#include "shooting.tpp"