OdeInt的stepper列表

Stepper overview

Table 1.6. Stepper Algorithms

Algorithm	Class	Concept	System Concept	Order	Error Estimation	Dense Output	Internal state	Remarks
Explicit Euler	euler	Dense Output Stepper	System	1	No	Yes	No	Very simple, only for demonstrating purpose
Modified Midpoint	modified_midpoint	Stepper	System	configurable (2)	No	No	No	Used in Bulirsch-Stoer implementation
Runge-Kutta 4	runge_kutta4	Stepper	System	4	No	No	No	The classical Runge-Kutta scheme, good general scheme without error control
Cash-Karp	runge_kutta_cash_karp54	Error Stepper	System	5	Yes (4)	No	No	Good general scheme with error estimation, to be used in controlled_error_stepper
Dormand-Prince 5	runge_kutta_dopri5	Error Stepper	System	5	Yes (4)	Yes	Yes	Standard method with error control and dense output, to be used in controlled_error_stepper and in dense_output_controlled_explicit_fsal.
Fehlberg 78	runge_kutta_fehlberg78	Error Stepper	System	8	Yes (7)	No	No	Good high order method with error estimation, to be used in controlled_error_stepper.
Adams Bashforth	adams_bashforth	Stepper	System	configurable	No	No	Yes	Multistep method
Adams Bashforth Moulton	adams_bashforth_moulton	Stepper	System	configurable	No	No	Yes	Combined multistep method
Controlled Runge-Kutta	controlled_runge_kutta	Controlled Stepper	System	depends	Yes	No	depends	Error control for Error Stepper. Requires an Error Stepper from above. Order depends on the given ErrorStepper
Dense Output Runge-Kutta	dense_output_runge_kutta	Dense Output Stepper	System	depends	No	Yes	Yes	Dense output for Stepper and Error Stepper from above if they provide dense output functionality (like euler and runge_kutta_dopri5). Order depends on the given stepper.
Bulirsch-Stoer	bulirsch_stoer	Controlled Stepper	System	variable	Yes	No	No	Stepper with step size and order control. Very good if high precision is required.
Bulirsch-Stoer Dense Output	bulirsch_stoer_dense_out	Dense Output Stepper	System	variable	Yes	Yes	No	Stepper with step size and order control as well as dense output. Very good if high precision and dense output is required.
Implicit Euler	implicit_euler	Stepper	Implicit System	1	No	No	No	Basic implicit routine. Requires the Jacobian. Works only with Boost.uBLAS vectors as state types.
Rosenbrock 4	rosenbrock4	Error Stepper	Implicit System	4	Yes	Yes	No	Good for stiff systems. Works only with Boost.uBLAS vectors as state types.
Controlled Rosenbrock 4	rosenbrock4_controller	Controlled Stepper	Implicit System	4	Yes	Yes	No	Rosenbrock 4 with error control. Works only with Boost.uBLAS vectors as state types.
Dense Output Rosenbrock 4	rosenbrock4_dense_output	Dense Output Stepper	Implicit System	4	Yes	Yes	No	Controlled Rosenbrock 4 with dense output. Works only with Boost.uBLAS vectors as state types.
Symplectic Euler	symplectic_euler	Stepper	Symplectic System Simple Symplectic System	1	No	No	No	Basic symplectic solver for separable Hamiltonian system
Symplectic RKN McLachlan	symplectic_rkn_sb3a_mclachlan	Stepper	Symplectic System Simple Symplectic System	4	No	No	No	Symplectic solver for separable Hamiltonian system with 6 stages and order 4.
Symplectic RKN McLachlan	symplectic_rkn_sb3a_m4_mclachlan	Stepper	Symplectic System Simple Symplectic System	4	No	No	No	Symplectic solver with 5 stages and order 4, can be used with arbitrary precision types.
Velocity Verlet	velocity_verlet	Stepper	Second Order System	1	No	No	Yes	Velocity verlet method suitable for molecular dynamics simulation.