4/5th Order Dormand–Prince Runge-Kutta ODE solver. More...

Inheritance diagram for RKDP45:

Collaboration diagram for RKDP45:

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Public Member Functions
	TypeName ("RKDP45")
	Runtime type information. More...

	RKDP45 (const ODESystem &ode, const dictionary &dict)
	Construct from ODE. More...

scalar	solve (const scalar x0, const scalarField &y0, const scalarField &dydx0, const scalar dx, scalarField &y) const
	Solve a single step dx and return the error. More...

void	solve (scalar &x, scalarField &y, scalar &dxTry) const
	Solve the ODE system and the update the state. More...

virtual void	solve (scalar &x, scalarField &y, scalar &dxTry) const
	Inherit solve from ODESolver. More...

virtual void	solve (scalar &x, scalarField &y, stepState &step) const
	Inherit solve from ODESolver. More...

virtual void	solve (const scalar xStart, const scalar xEnd, scalarField &y, scalar &dxEst) const
	Inherit solve from ODESolver. More...

Public Member Functions inherited from ODESolver
	TypeName ("ODESolver")
	Runtime type information. More...

	declareRunTimeSelectionTable (autoPtr, ODESolver, dictionary,(const ODESystem &ode, const dictionary &dict),(ode, dict))

	ODESolver (const ODESystem &ode, const dictionary &dict)
	Construct for given ODESystem. More...

	ODESolver (const ODESystem &ode, const scalarField &absTol, const scalarField &relTol)
	Construct for given ODESystem specifying tolerances. More...

virtual	~ODESolver ()
	Destructor. More...

scalarField &	absTol ()

scalarField &	relTol ()

virtual void	solve (scalar &x, scalarField &y, stepState &step) const
	Solve the ODE system as far as possible upto dxTry. More...

virtual void	solve (const scalar xStart, const scalar xEnd, scalarField &y, scalar &dxEst) const
	Solve the ODE system from xStart to xEnd, update the state. More...

Public Member Functions inherited from adaptiveSolver
	adaptiveSolver (const ODESystem &ode, const dictionary &dict)
	Construct from ODESystem. More...

virtual	~adaptiveSolver ()
	Destructor. More...

void	solve (const ODESystem &ode, scalar &x, scalarField &y, scalar &dxTry) const
	Solve the ODE system and the update the state. More...

Private Attributes
scalarField	yTemp_

scalarField	k2_

scalarField	k3_

scalarField	k4_

scalarField	k5_

scalarField	k6_

scalarField	err_
	Error-estimate field. More...

Static Private Attributes
static const scalar	c2 = 1.0/5.0
	RKDP Constants. More...

static const scalar	c3 = 3.0/10.0

static const scalar	c4 = 4.0/5.0

static const scalar	c5 = 8.0/9.0

static const scalar	a21 = 1.0/5.0

static const scalar	a31 = 3.0/40.0

static const scalar	a32 = 9.0/40.0

static const scalar	a41 = 44.0/45.0

static const scalar	a42 = -56.0/15.0

static const scalar	a43 = 32.0/9.0

static const scalar	a51 = 19372.0/6561.0

static const scalar	a52 = -25360.0/2187.0

static const scalar	a53 = 64448.0/6561.0

static const scalar	a54 = -212.0/729.0

static const scalar	a61 = 9017.0/3168.0

static const scalar	a62 = -355.0/33.0

static const scalar	a63 = 46732.0/5247.0

static const scalar	a64 = 49.0/176.0

static const scalar	a65 = -5103.0/18656.0

static const scalar	b1 = 35.0/384.0

static const scalar	b3 = 500.0/1113.0

static const scalar	b4 = 125.0/192.0

static const scalar	b5 = -2187.0/6784.0

static const scalar	b6 = 11.0/84.0

static const scalar	e1 = 5179.0/57600.0 - RKDP45::b1

static const scalar	e3 = 7571.0/16695.0 - RKDP45::b3

static const scalar	e4 = 393.0/640.0 - RKDP45::b4

static const scalar	e5 = -92097.0/339200.0 - RKDP45::b5

static const scalar	e6 = 187.0/2100.0 - RKDP45::b6

static const scalar	e7 = 1.0/40.0

Additional Inherited Members
Static Public Member Functions inherited from ODESolver
static autoPtr< ODESolver >	New (const ODESystem &ode, const dictionary &dict)
	Select null constructed. More...

Protected Member Functions inherited from ODESolver
scalar	normalizeError (const scalarField &y0, const scalarField &y, const scalarField &err) const
	Return the nomalized scalar error. More...

	ODESolver (const ODESolver &)
	Disallow default bitwise copy construct. More...

void	operator= (const ODESolver &)
	Disallow default bitwise assignment. More...

Protected Attributes inherited from ODESolver
const ODESystem &	odes_
	Reference to ODESystem. More...

label	n_
	Size of the ODESystem. More...

scalarField	absTol_
	Absolute convergence tolerance per step. More...

scalarField	relTol_
	Relative convergence tolerance per step. More...

label	maxSteps_
	The maximum number of sub-steps allowed for the integration step. More...

Detailed Description

4/5th Order Dormand–Prince Runge-Kutta ODE solver.

References:

    "A family of embedded Runge-Kutta formulae"
    Dormand, J. R.,
    Prince, P. J.,
    Journal of Computational and Applied Mathematics,
    6 (1), 1980: pp. 19-26.

    "Solving Ordinary Differential Equations I: Nonstiff Problems,
     second edition",
    Hairer, E.,
    Nørsett, S.,
    Wanner, G.,
    Springer-Verlag, Berlin. 1993, ISBN 3-540-56670-8.

See also: Foam::RKF45 Foam::RKCK45

Source files

Definition at line 69 of file RKDP45.H.

Constructor & Destructor Documentation

◆ RKDP45()

RKDP45	(	const ODESystem &	ode,
		const dictionary &	dict
	)

Construct from ODE.

Definition at line 79 of file RKDP45.C.

Member Function Documentation

◆ TypeName()

TypeName ( "RKDP45" )

Runtime type information.

◆ solve() [1/5]

Foam::scalar solve	(	const scalar	x0,
		const scalarField &	y0,
		const scalarField &	dydx0,
		const scalar	dx,
		scalarField &	y
	)		const

virtual

Solve a single step dx and return the error.

Implements adaptiveSolver.

Definition at line 96 of file RKDP45.C.

References Foam::constant::physicoChemical::c2, forAll, y, and Foam::y0().

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◆ solve() [2/5]

void solve	(	scalar &	x,
		scalarField &	y,
		scalar &	dxTry
	)		const

virtual

Solve the ODE system and the update the state.

Reimplemented from ODESolver.

Definition at line 164 of file RKDP45.C.

References adaptiveSolver::solve(), x, and y.

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◆ solve() [3/5]

virtual void solve

inline

Inherit solve from ODESolver.

Definition at line 178 of file ODESolver.H.

◆ solve() [4/5]

void solve

Inherit solve from ODESolver.

Definition at line 86 of file ODESolver.C.

◆ solve() [5/5]

void solve

Inherit solve from ODESolver.

Definition at line 99 of file ODESolver.C.

Field Documentation

◆ c2

const scalar c2 = 1.0/5.0

staticprivate

RKDP Constants.

Definition at line 78 of file RKDP45.H.

◆ c3

const scalar c3 = 3.0/10.0

staticprivate

Definition at line 78 of file RKDP45.H.

◆ c4

const scalar c4 = 4.0/5.0

staticprivate

Definition at line 78 of file RKDP45.H.

◆ c5

const scalar c5 = 8.0/9.0

staticprivate

Definition at line 78 of file RKDP45.H.