projects / ceph.git / blame
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1 | [/============================================================================ |
| 2 | Boost.odeint | |
| 3 | ||
| 4 | Copyright 2011-2013 Karsten Ahnert | |
| 5 | Copyright 2011 Mario Mulansky | |
| 6 | Copyright 2012 Sylwester Arabas | |
| 7 | ||
| 8 | Use, modification and distribution is subject to the Boost Software License, | |
| 9 | Version 1.0. (See accompanying file LICENSE_1_0.txt or copy at | |
| 10 | http://www.boost.org/LICENSE_1_0.txt) | |
| 11 | =============================================================================/] | |
| 12 | ||
| 13 | ||
| 14 | ||
| 15 | [section Error Stepper] | |
| 16 | ||
| 17 | This concepts specifies the interface an error stepper has to fulfill to be used within a ControlledErrorStepper. An error stepper must always fulfill the stepper concept. This can trivially implemented by | |
| 18 | ||
| 19 | `` | |
| 20 | template< class System > | |
| 21 | error_stepper::do_step( System sys , state_type &x , time_type t , time_type dt ) | |
| 22 | { | |
| 23 | state_type xerr; | |
| 24 | // allocate xerr | |
| 25 | do_step( sys , x , t , dt , xerr ); | |
| 26 | } | |
| 27 | `` | |
| 28 | ||
| 29 | [heading Description] | |
| 30 | ||
| 31 | An error stepper following this Error Stepper concept is capable of doing one step of the solution /x(t)/ of an ODE with step-size /dt/ to obtain /x(t+dt)/ and also computing an error estimate ['x[sub err]] of the result. | |
| 32 | Error Steppers can be Runge-Kutta steppers, symplectic steppers as well as implicit steppers. | |
| 33 | Based on the stepper type, the ODE is defined as __system, __symplectic_system, __simple_symplectic_system or __implicit_system. | |
| 34 | ||
| 35 | [heading Refinement of] | |
| 36 | ||
| 37 | * DefaultConstructable | |
| 38 | * CopyConstructable | |
| 39 | * Stepper | |
| 40 | ||
| 41 | [heading Associated types] | |
| 42 | ||
| 43 | * '''<para>'''[*state_type]'''</para>''' | |
| 44 | '''<para>'''`Stepper::state_type`'''</para>''' | |
| 45 | '''<para>'''The type characterizing the state of the ODE, hence ['x].'''</para>''' | |
| 46 | ||
| 47 | * '''<para>'''[*deriv_type]'''</para>''' | |
| 48 | '''<para>'''`Stepper::deriv_type`'''</para>''' | |
| 49 | '''<para>'''The type characterizing the derivative of the ODE, hence ['d x/dt].'''</para>''' | |
| 50 | ||
| 51 | * '''<para>'''[*time_type]'''</para>''' | |
| 52 | '''<para>'''`Stepper::time_type`'''</para>''' | |
| 53 | '''<para>'''The type characterizing the dependent variable of the ODE, hence the time ['t].'''</para>''' | |
| 54 | ||
| 55 | * '''<para>'''[*value_type]'''</para>''' | |
| 56 | '''<para>'''`Stepper::value_type`'''</para>''' | |
| 57 | '''<para>'''The numerical data type which is used within the stepper, something like `float`, `double`, `complex< double >`.'''</para>''' | |
| 58 | ||
| 59 | * '''<para>'''[*order_type]'''</para>''' | |
| 60 | '''<para>'''`Stepper::order_type`'''</para>''' | |
| 61 | '''<para>'''The type characterizing the order of the ODE, typically `unsigned short`.'''</para>''' | |
| 62 | ||
| 63 | * '''<para>'''[*stepper_category]'''</para>''' | |
| 64 | '''<para>'''`Stepper::stepper_category`'''</para>''' | |
| 65 | '''<para>'''A tag type characterizing the category of the stepper. This type must be convertible to `error_stepper_tag`.'''</para>''' | |
| 66 | ||
| 67 | ||
| 68 | [heading Notation] | |
| 69 | ||
| 70 | [variablelist | |
| 71 | [[`ErrorStepper`] [A type that is a model of Error Stepper]] | |
| 72 | [[`State`] [A type representing the state /x/ of the ODE]] | |
| 73 | [[`Error`] [A type representing the error calculated by the stepper, usually same as `State`]] | |
| 74 | [[`Time`] [A type representing the time /t/ of the ODE]] | |
| 75 | [[`stepper`] [An object of type `ErrorStepper`]] | |
| 76 | [[`x`] [Object of type `State`]] | |
| 77 | [[`xerr`] [Object of type `Error`]] | |
| 78 | [[`t`, `dt`] [Objects of type `Time`]] | |
| 79 | [[`sys`] [An object defining the ODE, should be a model of either __system, __symplectic_system, __simple_symplectic_system or __implicit_system.]] | |
| 80 | ] | |
| 81 | ||
| 82 | [heading Valid Expressions] | |
| 83 | ||
| 84 | [table | |
| 85 | [[Name] [Expression] [Type] [Semantics]] | |
| 86 | [[Get the stepper order] [`stepper.order()`] [`order_type`] [Returns the order of the stepper for one step without error estimation.]] | |
| 87 | [[Get the stepper order] [`stepper.stepper_order()`] [`order_type`] [Returns the order of the stepper for one error estimation step which is used for error calculation.]] | |
| 88 | [[Get the error order] [`stepper.errorr_order()`] [`order_type`] [Returns the order of the error step which is used for error calculation.]] | |
| 89 | [[Do step] [`stepper.do_step( sys , x , t , dt )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in-place to `x`.] ] | |
| 90 | [[Do step with error estimation] [`stepper.do_step( sys , x , t , dt , xerr )`] [`void`] [Performs one step of step size `dt` with error estimation. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.] ] | |
| 91 | [/ [Do step with reference] [`stepper.do_step( boost::ref(sys) , x , t , dt , xerr )`] [`void`] [Performs one step of step size `dt`. The newly obtained state is written in-place to `x` and the estimated error to `xerr`.] ] | |
| 92 | ] | |
| 93 | ||
| 94 | [heading Models] | |
| 95 | ||
| 96 | * `runge_kutta_cash_karp54` | |
| 97 | * `runge_kutta_dopri5` | |
| 98 | * `runge_kutta_fehlberg78` | |
| 99 | * `rosenbrock4` | |
| 100 | ||
| 101 | [endsect] |