/* * bulirsch_stoer.cpp * * Copyright 2009-2012 Karsten Ahnert * Copyright 2009-2012 Mario Mulansky * * Distributed under the Boost Software License, Version 1.0. * (See accompanying file LICENSE_1_0.txt or * copy at http://www.boost.org/LICENSE_1_0.txt) */ #include <iostream> #include <fstream> #define _USE_MATH_DEFINES #include <cmath> #include <boost/array.hpp> #include <boost/ref.hpp> #include <boost/numeric/odeint/config.hpp> #include <boost/numeric/odeint.hpp> #include <boost/numeric/odeint/stepper/bulirsch_stoer.hpp> #include <boost/numeric/odeint/stepper/bulirsch_stoer_dense_out.hpp> using namespace std; using namespace boost::numeric::odeint; typedef boost::array< double , 1 > state_type; /* * x' = ( - x*sin t + 2 tan x ) y * with x( pi/6 ) = 2/sqrt(3) the analytic solution is 1/cos t */ void rhs( const state_type &x , state_type &dxdt , const double t ) { dxdt[0] = ( - x[0] * sin( t ) + 2.0 * tan( t ) ) * x[0]; } void rhs2( const state_type &x , state_type &dxdt , const double t ) { dxdt[0] = sin(t); } ofstream out; void write_out( const state_type &x , const double t ) { out << t << '\t' << x[0] << endl; } int main() { bulirsch_stoer_dense_out< state_type > stepper( 1E-8 , 0.0 , 0.0 , 0.0 ); bulirsch_stoer< state_type > stepper2( 1E-8 , 0.0 , 0.0 , 0.0 ); state_type x = {{ 2.0 / sqrt(3.0) }}; double t = M_PI/6.0; //double t = 0.0; double dt = 0.01; double t_end = M_PI/2.0 - 0.1; //double t_end = 100.0; out.open( "bs.dat" ); out.precision(16); integrate_const( stepper , rhs , x , t , t_end , dt , write_out ); out.close(); x[0] = 2.0 / sqrt(3.0); out.open( "bs2.dat" ); out.precision(16); integrate_adaptive( stepper , rhs , x , t , t_end , dt , write_out ); out.close(); x[0] = 2.0 / sqrt(3.0); out.open( "bs3.dat" ); out.precision(16); integrate_adaptive( stepper2 , rhs , x , t , t_end , dt , write_out ); out.close(); typedef runge_kutta_dopri5< state_type > dopri5_type; typedef controlled_runge_kutta< dopri5_type > controlled_dopri5_type; typedef dense_output_runge_kutta< controlled_dopri5_type > dense_output_dopri5_type; dense_output_dopri5_type dopri5( controlled_dopri5_type( default_error_checker< double >( 1E-2 , 0.0 , 0.0 , 0.0 ) ) ); x[0] = 2.0 / sqrt(3.0); out.open( "bs4.dat" ); out.precision(16); integrate_adaptive( dopri5 , rhs , x , t , t_end , dt , write_out ); out.close(); }