MFTPBVPMF
[MFImplicitMF]

Collaboration diagram for MFTPBVPMF:

Typedefs
typedef void(*	MFTPBVPFFUNCTION )(double, int, double *, int, double *, double *, double *, double *, MFErrorHandler e)
	A function defining the right hand side of a two point boundary value problem.
typedef void(*	MFTPBVPAFUNCTION )(int, int, double *, double *, int, double *, double *, double *, double *, double *, MFErrorHandler e)
	A function defining the boundary value equations of a two point boundary value problem.
typedef void(*	MFTPBVPLFUNCTION )(int, double, int, double *, int, double *, double *, double *, double *, MFErrorHandler e)
	A function defining the integral piece of an integral constraint of a two point boundary value problem.
typedef void(*	MFTPBVPMFUNCTION )(int, int, double *, double *, double *, MFErrorHandler e)
	A function defining the non-vector piece of an integral constraint of a two point boundary value problem.
Functions
FImplicitMF	MFIMFCreateTPBVP (int k, int nx, int nu, int np, MFTPBVPFFUNCTION f, MFTPBVPFFUNCTION fu, MFTPBVPFFUNCTION fl, int nbc, MFTPBVPAFUNCTION a, MFTPBVPAFUNCTION au, MFTPBVPAFUNCTION al, int nic, MFTPBVPLFUNCTION l, MFTPBVPLFUNCTION lu, MFTPBVPLFUNCTION ll, MFTPBVPMFUNCTION m, MFTPBVPMFUNCTION ml, MFErrorHandler e)
	Creates a manifold which is the solution manifold of a two point boundary value problem with integral constraints. Keller's second order box scheme is used.
MFNVector	MFTPBVPIntegrateForInitialSolution (MFImplicitMF M, double *u0, double *p, double *x, MFErrorHandler e)
	Solves an initial value problem in place of a MFTPBVPMF, and returns the solution. This may be useful in constructing initial guesses.
MFNVector	MFTPBVPIntegrateForTangent (MFImplicitMF M, MFNVector u, double *du0, double *dp, MFErrorHandler e)
	Solves an initial value problem of the linearization of a MFTPBVPMF, and returns the solution. This may be useful in constructing initial approximations of the columns of the basis for the tangent space.
void	MFTPBVPSetEpsilon (MFImplicitMF M, double epsilon, MFErrorHandler e)
	Sets the tolerance on the distance between a linear approximation at the center of a chart and the manifold.

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Function Documentation

MFImplicitMF MFIMFCreateTPBVP (  int  k, int  nx, int  nu, int  np, MFTPBVPFFUNCTION  f, MFTPBVPFFUNCTION  fu, MFTPBVPFFUNCTION  fl, int  nbc, MFTPBVPAFUNCTION  a, MFTPBVPAFUNCTION  au, MFTPBVPAFUNCTION  al, int  nic, MFTPBVPLFUNCTION  l, MFTPBVPLFUNCTION  lu, MFTPBVPLFUNCTION  ll, MFTPBVPMFUNCTION  m, MFTPBVPMFUNCTION  ml, MFErrorHandler  e )

Creates a manifold which is the solution manifold of a two point boundary value problem with integral constraints. Keller's second order box scheme is used. Parameters: k  The number of degrees of freedom (the dimension of the solution manifold). nx  The number of mesh intervals to use in the discretization. nu  The number of functions defined on the mesh. np  The number of scalar parameters. f  The right hand siade of the ODE's u'=f(u,p). fu  The first derivatives of the right hand side with respect to u. fl  The first derivatives of the right hand side with respect to the parameters l. nbc  The number of boundary conditions. a  The function which defines the boundary conditions a(u(0),u(1),p)=0 au  The derivative of the boundary conditions with respect to u. al  The derivative of the boundary conditions with respect to the parameters l. nic  The number of integral conditions l  The function which defines the integral part of the integral conditions int_0^1 l(u(t),p) dt + m(l)=0 lu  The derivative of the integral part of the integral conditions with respect to u. ll  The derivative of the integral part of the integral conditions with respect to the parameters l. m  The function which defines the non-integral part of the integral conditions int_0^1 l(u(t),p) dt + m(l)=0 ml  The derivative of the non-integral part of the integral conditions with respect to the parameters l. e  A place to return errors. Returns: An implicitly defined manifold.

MFNVector MFTPBVPIntegrateForInitialSolution (  MFImplicitMF  M, double *  u0, double *  p, double *  x, MFErrorHandler  e )

Solves an initial value problem in place of a MFTPBVPMF, and returns the solution. This may be useful in constructing initial guesses. Parameters: M  An MFTPBVPMF u0  An array of length nu with the initial condition. p  An array of length nl with the parameter values. x  The nx+1 mesh points on [0,1]. e  A place to return errors. Returns: A solution (u(t),p).

MFNVector MFTPBVPIntegrateForTangent (  MFImplicitMF  M, MFNVector  u, double *  du0, double *  dp, MFErrorHandler  e )

Solves an initial value problem of the linearization of a MFTPBVPMF, and returns the solution. This may be useful in constructing initial approximations of the columns of the basis for the tangent space. Parameters: M  An MFTPBVPMF u  A solution (u(t),p) which is the "point" at which the variational equations are written. du0  The initial perturbation (at x=0). dp  The perturbation of the parameters. e  A place to return errors. Returns: A solution (du(t),dp) that might be used as a basis vector for the tangent space.

void MFTPBVPSetEpsilon (  MFImplicitMF  M, double  epsilon, MFErrorHandler  e )

Sets the tolerance on the distance between a linear approximation at the center of a chart and the manifold. Parameters: M  An MFTPBVPMF epsilon  The value for the parameter epsilon. e  A place to return errors.

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