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[/============================================================================
Boost.odeint
Copyright 2011-2012 Karsten Ahnert
Copyright 2011-2012 Mario Mulansky
Use, modification and distribution is subject to 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)
=============================================================================/]
[table Adaptive step size algorithms
[ [Stepper] [Tolerance formula] [Norm] [Step size adaption] ]
[ [`controlled_runge_kutta`]
[
['val = || | err[subl i] | / ( __epsilon[subl abs] + __epsilon[subl rel] * ( a[subl x] | x[subl i] | + a[subl dxdt] | | dxdt[subl i] | )|| ]
]
[['||x|| = max( x[subl i] )]]
[
['val > 1 : dt[subl new] = dt[subl current] max( 0.9 pow( val , -1 / ( O[subl E] - 1 ) ) , 0.2 )]
['val < 0.5 : dt[subl new] = dt[subl current] min( 0.9 pow( val , -1 / O[subl S] ) , 5 )]
['else : dt[subl new] = dt[subl current]]
] ]
[ [`rosenbrock4_controller`]
[
['val = || err[subl i] / ( __epsilon[subl abs] + __epsilon[subl rel] max( | x[subl i] | , | xold[subl i] | ) ) || ]
]
[['||x||=(__Sigma[subl i] x[subl i][super 2])[super 1/2]]]
[
['fac = max( 1 / 6 , min( 5 , pow( val , 1 / 4 ) / 0.9 ) ]
['fac2 = max( 1 / 6 , min( 5 , dt[subl old] / dt[subl current] pow( val[super 2] / val[subl old] , 1 / 4 ) / 0.9 ) ]
['val > 1 : dt[subl new] = dt[subl current] / fac ]
['val < 1 : dt[subl new] = dt[subl current] / max( fac , fac2 ) ]
]
]
[ [bulirsch_stoer] [['tol=1/2]] [-] [['dt[subl new] = dt[subl old][super 1/a]]] ]
]
[/
safe = 0.9 , fac1 = 5.0 , fac2 = 1.0 / 6.0
value_type fac_pred = ( m_dt_old / dt ) * pow( err * err / m_err_old , 0.25 ) / safe;
fac_pred = std::max( fac2 , std::min( fac1 , fac_pred ) );
fac = std::max( fac , fac_pred );
dt_new = dt / fac;
fac = max( fac2 , min( fac1 , pow( err , 0.25 ) / safe ) )
]
|
