belfem::ode Namespace Reference

Classes
class	BDF
class	Integrator
class	ODE
	an object that can create an ordinary differential equation More...

Enumerations
enum class	Status { OK = 0 , TRAPPED = 1 , MAXIT = 2 }
enum class	Type { RK45 = 0 , DOP853 = 1 }

Functions
void	DOP853_init (ODE &aODE, Cell< Vector< real > > &aWork)
Status	DOP853 (ODE &aODE, real &aT, Vector< real > &aY, real &aStep, Cell< Vector< real > > &aWork, const real aEpsilon=1e-7, const uint aMaxIterations=1000, const real aTmax=BELFEM_REAL_MAX, const bool aAutoTimestep=true)
	Dormand-Prince 8(5,3) explicit Runge-Kutta method (DOP853).
void	RK45_init (ODE &aODE, Cell< Vector< real > > &aWork)
Status	RK45 (ODE &aODE, real &aT, Vector< real > &aY, real &aStep, Cell< Vector< real > > &aWork, const real aEpsilon, const uint aMaxIterations, const real aTmax, const bool aAutoTimestep)

Enumeration Type Documentation

Status

enum class belfem::ode::Status

strong

Enumerator
OK
TRAPPED
MAXIT

Type

enum class belfem::ode::Type

strong

Enumerator
RK45
DOP853

Function Documentation

DOP853()

Status belfem::ode::DOP853	(	ODE &	aODE,
		real &	aT,
		Vector< real > &	aY,
		real &	aStep,
		Cell< Vector< real > > &	aWork,
		const real	aEpsilon = 1e-7,
		const uint	aMaxIterations = 1000,
		const real	aTmax = BELFEM_REAL_MAX,
		const bool	aAutoTimestep = true )

Dormand-Prince 8(5,3) explicit Runge-Kutta method (DOP853).

An 8th order method with embedded 5th and 3rd order error estimators. The step size controller uses the 5th order estimator. Recommended for smooth, non-stiff problems requiring high accuracy (tolerances tighter than ~1e-8). For moderate accuracy, RK45 is more efficient.

Reference: Hairer, Norsett, Wanner: Solving Ordinary Differential Equations I, 2nd ed., Springer (1993), Section II.6.

DOP853_init()

void belfem::ode::DOP853_init	(	ODE &	aODE,
		Cell< Vector< real > > &	aWork )

RK45()

Status belfem::ode::RK45	(	ODE &	aODE,
		real &	aT,
		Vector< real > &	aY,
		real &	aStep,
		Cell< Vector< real > > &	aWork,
		const real	aEpsilon,
		const uint	aMaxIterations,
		const real	aTmax,
		const bool	aAutoTimestep )

RK45_init()

void belfem::ode::RK45_init	(	ODE &	aODE,
		Cell< Vector< real > > &	aWork )