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55 lines
2.0 KiB
Plaintext
55 lines
2.0 KiB
Plaintext
[/============================================================================
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Boost.odeint
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Copyright 2011-2012 Karsten Ahnert
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Copyright 2011-2012 Mario Mulansky
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Use, modification and distribution is subject to the Boost Software License,
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Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at
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http://www.boost.org/LICENSE_1_0.txt)
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=============================================================================/]
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[table Adaptive step size algorithms
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[ [Stepper] [Tolerance formula] [Norm] [Step size adaption] ]
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[ [`controlled_runge_kutta`]
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[
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['val = || | err[subl i] | / ( __epsilon[subl abs] + __epsilon[subl rel] * ( a[subl x] | x[subl i] | + a[subl dxdt] | | dxdt[subl i] | )|| ]
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]
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[['||x|| = max( x[subl i] )]]
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[
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['val > 1 : dt[subl new] = dt[subl current] max( 0.9 pow( val , -1 / ( O[subl E] - 1 ) ) , 0.2 )]
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['val < 0.5 : dt[subl new] = dt[subl current] min( 0.9 pow( val , -1 / O[subl S] ) , 5 )]
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['else : dt[subl new] = dt[subl current]]
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] ]
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[ [`rosenbrock4_controller`]
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[
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['val = || err[subl i] / ( __epsilon[subl abs] + __epsilon[subl rel] max( | x[subl i] | , | xold[subl i] | ) ) || ]
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]
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[['||x||=(__Sigma[subl i] x[subl i][super 2])[super 1/2]]]
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[
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['fac = max( 1 / 6 , min( 5 , pow( val , 1 / 4 ) / 0.9 ) ]
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['fac2 = max( 1 / 6 , min( 5 , dt[subl old] / dt[subl current] pow( val[super 2] / val[subl old] , 1 / 4 ) / 0.9 ) ]
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['val > 1 : dt[subl new] = dt[subl current] / fac ]
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['val < 1 : dt[subl new] = dt[subl current] / max( fac , fac2 ) ]
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]
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]
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[ [bulirsch_stoer] [['tol=1/2]] [-] [['dt[subl new] = dt[subl old][super 1/a]]] ]
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]
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[/
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safe = 0.9 , fac1 = 5.0 , fac2 = 1.0 / 6.0
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value_type fac_pred = ( m_dt_old / dt ) * pow( err * err / m_err_old , 0.25 ) / safe;
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fac_pred = std::max( fac2 , std::min( fac1 , fac_pred ) );
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fac = std::max( fac , fac_pred );
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dt_new = dt / fac;
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fac = max( fac2 , min( fac1 , pow( err , 0.25 ) / safe ) )
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] |