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Diffstat (limited to 'src/boost/libs/numeric/odeint/examples/abm_precision.cpp')
-rw-r--r-- | src/boost/libs/numeric/odeint/examples/abm_precision.cpp | 84 |
1 files changed, 84 insertions, 0 deletions
diff --git a/src/boost/libs/numeric/odeint/examples/abm_precision.cpp b/src/boost/libs/numeric/odeint/examples/abm_precision.cpp new file mode 100644 index 00000000..747919f3 --- /dev/null +++ b/src/boost/libs/numeric/odeint/examples/abm_precision.cpp @@ -0,0 +1,84 @@ +/* + * abm_precision.cpp + * + * example to check the order of the multi-step methods + * + * Copyright 2009-2013 Karsten Ahnert + * Copyright 2009-2013 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 <cmath> + +#include <boost/array.hpp> +#include <boost/numeric/odeint.hpp> + +using namespace boost::numeric::odeint; + +const int Steps = 4; + +typedef double value_type; + +typedef boost::array< double , 2 > state_type; + +typedef runge_kutta_fehlberg78<state_type> initializing_stepper_type; +typedef adams_bashforth_moulton< Steps , state_type > stepper_type; +//typedef adams_bashforth< Steps , state_type > stepper_type; + +// harmonic oscillator, analytic solution x[0] = sin( t ) +struct osc +{ + void operator()( const state_type &x , state_type &dxdt , const double t ) const + { + dxdt[0] = x[1]; + dxdt[1] = -x[0]; + } +}; + +int main() +{ + stepper_type stepper; + initializing_stepper_type init_stepper; + const int o = stepper.order()+1; //order of the error is order of approximation + 1 + + const state_type x0 = {{ 0.0 , 1.0 }}; + state_type x1 = x0; + double t = 0.0; + double dt = 0.25; + // initialization, does a number of steps already to fill internal buffer, t is increased + // we use the rk78 as initializing stepper + stepper.initialize( boost::ref(init_stepper) , osc() , x1 , t , dt ); + // do a number of steps to fill the buffer with results from adams bashforth + for( size_t n=0 ; n < stepper.steps ; ++n ) + { + stepper.do_step( osc() , x1 , t , dt ); + t += dt; + } + double A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] ); + double phi = std::asin(x1[0]/A) - t; + // now we do the actual step + stepper.do_step( osc() , x1 , t , dt ); + // only examine the error of the adams-bashforth-moulton step, not the initialization + const double f = 2.0 * std::abs( A*sin(t+dt+phi) - x1[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 ) + { + x1 = x0; + t = 0.0; + stepper.initialize( boost::ref(init_stepper) , osc() , x1 , t , dt ); + A = std::sqrt( x1[0]*x1[0] + x1[1]*x1[1] ); + phi = std::asin(x1[0]/A) - t; + // now we do the actual step + stepper.do_step( osc() , x1 , t , dt ); + // only examine the error of the adams-bashforth-moulton step, not the initialization + std::cout << dt << '\t' << std::abs( A*sin(t+dt+phi) - x1[0] ) << std::endl; + dt *= 0.5; + } +} |