Classes
class	BasicC2OdeSolver

class	BasicCnOdeSolver

class	BasicFadOdeSolver

class	BasicOdeSolver
	MapT constraints: type definitions: More...

class	C1DynSys

class	C2DynSys

class	C2OdeSolver

class	CnDynSys

class	CnOdeSolver

class	Linear2d

class	Linear3d

class	OdeNumTaylor

class	VLin3D

class	DiscreteDynSys
	DiscreteDynSys is a proxy to convert any Map into discrete Dynamical System. More...

class	FlowballSet

class	DynSys
	Class dynsys is an abstract class representing a discrete dynamical system. More...

class	HOSolver

class	DynSysMap
	DynSysMap is a proxy to convert any Map into discrete Dynamical System. More...

class	FadFunction

class	FadMap

class	LorenzFadMap
	Sample implementation of FadMap. This class implements the vector field for the Lorenz system. Template parameters are: Scalar: double, interval, MpFloat, MpInterval, etc. D: in this case either 3 or 0. If D=3 then vectors and matrices are allocated on stack and the computations are much faster but we must know they dimension at compile time. This forces separate compilation of all the classes like vectors and matrices for this particular dimension. D=0 means that vectors and matrices are allocated on the storage and they can be of arbitrary dimension specified at runtime. More...

class	LorenzSection

class	FadOdeSolver

class	FirstOrderEnclosure

class	HighOrderEnclosure
	This file defines class for computation of [C0-C2] rough enclosure to an ODE by high order Taylor method. More...

struct	C1SetMove

struct	C1SetMove< T, SetT, false >

struct	C2SetMove

struct	C2SetMove< T, SetT, false >

struct	CnSetMove

struct	CnSetMove< T, SetT, false >

struct	C1JetMove

struct	C1JetMove< T, JetT, false >

struct	C2JetMove

struct	C2JetMove< T, JetT, false >

struct	CnJetMove

struct	CnJetMove< T, JetT, false >

class	MpLastTermsStepControl

class	StepControlInterface< MpLastTermsStepControl, Scalar >
	This class is a common interface for StepControl used in PoincareMap and TimeMap. Both classes inherit this interface. More...

class	OdeSolver

class	OdeTraits
	Defines characteristic traits of ODE. More...

class	SolverException

class	StepControlInterface
	This class is a common interface for StepControl used in PoincareMap and TimeMap. Both classes inherit this interface. More...

class	NoStepControlInterface

class	NoStepControl
	This class provides an empty time step control for the solutions to ODEs. It contains an interface for other implementations of TSC. More...

class	StepControlInterface< NoStepControl, double >

class	FixedStepControl

class	ILastTermsStepControl

class	DLastTermsStepControl

class	IEncFoundStepControl

Functions
template<class Solver , class RemainderType >
void	computeAndApproveRemainder (Solver &solver, const typename Solver::ScalarType &t, const typename Solver::VectorType &xx, RemainderType &o_rem, RemainderType &o_enc)

template<typename MapType >
DiscreteDynSys< MapType >	makeDiscreteDynSys (const MapType &map)
	Makes DiscreteDynSys object from given map. Template parameters are recognized automatically. More...

template<typename MapType >
DynSysMap< MapType >	makeDynSysMap (const MapType &map)
	Makes DynSysMap object from given map. Template parameters are recognized automatically. More...

template<class Solver >
Solver::ScalarType	computeNextStep (Solver &solver, int numberOfTerms, const typename TypeTraits< typename Solver::ScalarType >::Real &epsilon, const typename TypeTraits< typename Solver::ScalarType >::Real &minTimeStep, int degree, bool clearMantissaFlag)
	Computes next time step using already computed Taylor series of the solution. More...

template<class Real >
Real	clearMantissaBits (Real step, int maxValue=32)
	the following function clears the last bits of mantissa More...

template<class Solver >
Solver::ScalarType	computeNextStep (Solver &solver, int numberOfTerms, const typename TypeTraits< typename Solver::ScalarType >::Real &epsilon, const typename TypeTraits< typename Solver::ScalarType >::Real &minTimeStep, int degree)
	Computes next time step using already computed Taylor series of the solution. More...

Function Documentation

◆ clearMantissaBits()

template<class Real >

Real capd::dynsys::clearMantissaBits	(	Real	step,
		int	maxValue = `32`
	)

the following function clears the last bits of mantissa

◆ computeNextStep() [1/2]

template<class Solver >

Solver::ScalarType capd::dynsys::computeNextStep	(	Solver &	solver,
		int	numberOfTerms,
		const typename TypeTraits< typename Solver::ScalarType >::Real &	epsilon,
		const typename TypeTraits< typename Solver::ScalarType >::Real &	minTimeStep,
		int	degree
	)

Computes next time step using already computed Taylor series of the solution.

We choose time step so that expected error of the next step of the ODE integration is less than epsilon.

Remarks: For non rigorous computations it is good to take more that one term to prevent big time steps when the last term happens to be close to zero

Parameters

solver	ODE solver containing Taylor series of the solution for current step
numberOfTerms	number of terms in Taylor series to use in predictions
epsilon	expected error for one step of integration
minTimeStep	minimal time step allowed

◆ computeNextStep() [2/2]