94 lines
2.4 KiB
C++
94 lines
2.4 KiB
C++
/* Boost numeric test of the runge kutta steppers test file
|
|
|
|
Copyright 2012 Mario Mulansky
|
|
Copyright 2012 Karsten Ahnert
|
|
|
|
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)
|
|
*/
|
|
|
|
// disable checked iterator warning for msvc
|
|
#include <boost/config.hpp>
|
|
#ifdef BOOST_MSVC
|
|
#pragma warning(disable:4996)
|
|
#endif
|
|
|
|
#define BOOST_TEST_MODULE numeric_runge_kutta
|
|
|
|
#include <iostream>
|
|
#include <cmath>
|
|
|
|
#include <boost/array.hpp>
|
|
|
|
#include <boost/test/unit_test.hpp>
|
|
|
|
#include <boost/mpl/vector.hpp>
|
|
|
|
#include <boost/numeric/odeint.hpp>
|
|
|
|
using namespace boost::unit_test;
|
|
using namespace boost::numeric::odeint;
|
|
namespace mpl = boost::mpl;
|
|
|
|
typedef double value_type;
|
|
|
|
typedef boost::array< double , 1 > state_type;
|
|
|
|
// harmonic oscillator, analytic solution x[0] = sin( t )
|
|
struct osc
|
|
{
|
|
void operator()( const state_type &x, const state_type &v, state_type &a,
|
|
const double t ) const
|
|
{
|
|
a[0] = -x[0];
|
|
}
|
|
};
|
|
|
|
BOOST_AUTO_TEST_SUITE( velocity_verlet_test )
|
|
|
|
BOOST_AUTO_TEST_CASE( numeric_velocity_verlet_test )
|
|
{
|
|
|
|
velocity_verlet<state_type> stepper;
|
|
const int steps = 10;
|
|
// order of the error is order of approximation + 1
|
|
const int o = stepper.order() + 1;
|
|
|
|
const state_type x0 = {{ 0.0 }};
|
|
const state_type v0 = {{ 1.0 }};
|
|
state_type x = x0;
|
|
state_type v = v0;
|
|
const double t = 0.0;
|
|
/* do a first step with dt=0.1 to get an estimate on the prefactor of the error dx = f * dt^(order+1) */
|
|
double dt = 0.5;
|
|
for ( int step = 0; step < steps; ++step )
|
|
{
|
|
stepper.do_step(
|
|
osc(), std::make_pair( boost::ref( x ), boost::ref( v ) ), t, dt );
|
|
}
|
|
const double f = steps * std::abs( sin( steps * dt ) - x[0] ) /
|
|
std::pow( dt, o ); // upper bound
|
|
|
|
std::cout << o << " , " << f << std::endl;
|
|
|
|
/* as long as we have errors above machine precision */
|
|
while( f*std::pow( dt , o ) > 1E-16 )
|
|
{
|
|
x = x0;
|
|
v = v0;
|
|
stepper.reset();
|
|
for ( int step = 0; step < steps; ++step )
|
|
{
|
|
stepper.do_step( osc() , std::make_pair(boost::ref(x), boost::ref(v)) , t , dt );
|
|
}
|
|
std::cout << "Testing dt=" << dt << std::endl;
|
|
BOOST_CHECK_LT( std::abs( sin( steps * dt ) - x[0] ),
|
|
f * std::pow( dt, o ) );
|
|
dt *= 0.5;
|
|
}
|
|
};
|
|
|
|
|
|
BOOST_AUTO_TEST_SUITE_END()
|