1[/============================================================================ 2 Boost.odeint 3 4 Copyright 2011-2012 Karsten Ahnert 5 Copyright 2011-2012 Mario Mulansky 6 7 Use, modification and distribution is subject to the Boost Software License, 8 Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at 9 http://www.boost.org/LICENSE_1_0.txt) 10=============================================================================/] 11 12[table Adaptive step size algorithms 13 [ [Stepper] [Tolerance formula] [Norm] [Step size adaption] ] 14 [ [`controlled_runge_kutta`] 15 [ 16 ['val = || | err[subl i] | / ( __epsilon[subl abs] + __epsilon[subl rel] * ( a[subl x] | x[subl i] | + a[subl dxdt] | | dxdt[subl i] | )|| ] 17 ] 18 [['||x|| = max( x[subl i] )]] 19 [ 20 ['val > 1 : dt[subl new] = dt[subl current] max( 0.9 pow( val , -1 / ( O[subl E] - 1 ) ) , 0.2 )] 21 22 ['val < 0.5 : dt[subl new] = dt[subl current] min( 0.9 pow( val , -1 / O[subl S] ) , 5 )] 23 24 ['else : dt[subl new] = dt[subl current]] 25 ] ] 26 [ [`rosenbrock4_controller`] 27 [ 28 ['val = || err[subl i] / ( __epsilon[subl abs] + __epsilon[subl rel] max( | x[subl i] | , | xold[subl i] | ) ) || ] 29 ] 30 [['||x||=(__Sigma[subl i] x[subl i][super 2])[super 1/2]]] 31 [ 32 ['fac = max( 1 / 6 , min( 5 , pow( val , 1 / 4 ) / 0.9 ) ] 33 34 ['fac2 = max( 1 / 6 , min( 5 , dt[subl old] / dt[subl current] pow( val[super 2] / val[subl old] , 1 / 4 ) / 0.9 ) ] 35 36 ['val > 1 : dt[subl new] = dt[subl current] / fac ] 37 38 ['val < 1 : dt[subl new] = dt[subl current] / max( fac , fac2 ) ] 39 ] 40 ] 41 [ [bulirsch_stoer] [['tol=1/2]] [-] [['dt[subl new] = dt[subl old][super 1/a]]] ] 42] 43 44[/ 45 46safe = 0.9 , fac1 = 5.0 , fac2 = 1.0 / 6.0 47 48value_type fac_pred = ( m_dt_old / dt ) * pow( err * err / m_err_old , 0.25 ) / safe; 49 fac_pred = std::max( fac2 , std::min( fac1 , fac_pred ) ); 50 fac = std::max( fac , fac_pred ); 51 dt_new = dt / fac; 52 53 54fac = max( fac2 , min( fac1 , pow( err , 0.25 ) / safe ) ) 55]