c23fdbeb8f
extrapolation stepper has a configurable order, so we can use it as initializing stepper in the adams-bashforth algorithm. All numeric tests pass.
118 lines
3.6 KiB
C++
118 lines
3.6 KiB
C++
/* Boost numeric test of the adams-bashforth steppers test file
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Copyright 2013 Karsten Ahnert
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Copyright 2013-2015 Mario Mulansky
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Distributed under the Boost Software License, Version 1.0.
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(See accompanying file LICENSE_1_0.txt or
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copy at http://www.boost.org/LICENSE_1_0.txt)
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*/
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// disable checked iterator warning for msvc
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#include <boost/config.hpp>
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#ifdef BOOST_MSVC
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#pragma warning(disable:4996)
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#endif
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#define BOOST_TEST_MODULE numeric_adams_bashforth
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#include <iostream>
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#include <cmath>
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#include <boost/array.hpp>
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#include <boost/test/unit_test.hpp>
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#include <boost/mpl/vector.hpp>
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#include <boost/numeric/odeint.hpp>
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using namespace boost::unit_test;
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using namespace boost::numeric::odeint;
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namespace mpl = boost::mpl;
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typedef double value_type;
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typedef boost::array< double , 2 > state_type;
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// harmonic oscillator, analytic solution x[0] = sin( t )
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struct osc
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{
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void operator()( const state_type &x , state_type &dxdt , const double t ) const
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{
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dxdt[0] = x[1];
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dxdt[1] = -x[0];
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}
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};
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BOOST_AUTO_TEST_SUITE( numeric_adams_bashforth_test )
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/* generic test for all adams bashforth steppers */
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template< class Stepper >
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struct perform_adams_bashforth_test
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{
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void operator()( void )
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{
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Stepper stepper;
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const int o = stepper.order()+1; //order of the error is order of approximation + 1
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const state_type x0 = {{ 0.0 , 1.0 }};
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state_type x1 = x0;
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double t = 0.0;
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double dt = 0.2;
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// initialization, does a number of steps already to fill internal buffer, t is increased
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stepper.initialize( osc() , x1 , t , dt );
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double A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] );
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double phi = std::asin(x1[0]/A) - t;
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// do a number of steps to fill the buffer with results from adams bashforth
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for( size_t n=0 ; n < stepper.steps ; ++n )
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{
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stepper.do_step( osc() , x1 , t , dt );
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t += dt;
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}
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// now we do the actual step
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stepper.do_step( osc() , x1 , t , dt );
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// only examine the error of the adams-bashforth step, not the initialization
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const double f = 2.0 * std::abs( A*sin(t+dt+phi) - x1[0] ) / std::pow( dt , o ); // upper bound
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std::cout << o << " , "
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<< Stepper::initializing_stepper_type::order_value+1 << " , "
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<< f << std::endl;
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/* as long as we have errors above machine precision */
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while( f*std::pow( dt , o ) > 1E-16 )
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{
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x1 = x0;
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t = 0.0;
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stepper.initialize( osc() , x1 , t , dt );
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A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] );
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phi = std::asin(x1[0]/A) - t;
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// now we do the actual step
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stepper.do_step( osc() , x1 , t , dt );
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// only examine the error of the adams-bashforth step, not the initialization
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std::cout << "Testing dt=" << dt << " , " << std::abs( A*sin(t+dt+phi) - x1[0] ) << std::endl;
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BOOST_CHECK_LT( std::abs( A*sin(t+dt+phi) - x1[0] ) , f*std::pow( dt , o ) );
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dt *= 0.5;
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}
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}
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};
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typedef mpl::vector<
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adams_bashforth< 2 , state_type > ,
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adams_bashforth< 3 , state_type > ,
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adams_bashforth< 4 , state_type > ,
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adams_bashforth< 5 , state_type > ,
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adams_bashforth< 6 , state_type > ,
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adams_bashforth< 7 , state_type > ,
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adams_bashforth< 8 , state_type >
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> adams_bashforth_steppers;
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BOOST_AUTO_TEST_CASE_TEMPLATE( adams_bashforth_test , Stepper, adams_bashforth_steppers )
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{
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perform_adams_bashforth_test< Stepper > tester;
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tester();
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}
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BOOST_AUTO_TEST_SUITE_END()
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