oomph::Orthpoly Namespace Reference

## Functions

void gll_nodes (const unsigned &Nnode, Vector< double > &x)
Calculates the Gauss Lobatto Legendre abscissas for degree p = NNode-1. More...

void gll_nodes (const unsigned &Nnode, Vector< double > &x, Vector< double > &w)

void gl_nodes (const unsigned &Nnode, Vector< double > &x)

void gl_nodes (const unsigned &Nnode, Vector< double > &x, Vector< double > &w)

double legendre (const unsigned &p, const double &x)
Calculates Legendre polynomial of degree p at x using the three term recurrence relation . More...

void legendre_vector (const unsigned &p, const double &x, Vector< double > &polys)
Calculates Legendre polynomial of degree p at x using three term recursive formula. Returns all polynomials up to order p in the vector. More...

double dlegendre (const unsigned &p, const double &x)
Calculates first derivative of Legendre polynomial of degree p at x using three term recursive formula. . More...

double ddlegendre (const unsigned &p, const double &x)
Calculates second derivative of Legendre polynomial of degree p at x using three term recursive formula. More...

double jacobi (const int &alpha, const int &beta, const unsigned &p, const double &x)
Calculate the Jacobi polnomials. More...

void jacobi (const int &alpha, const int &beta, const unsigned &p, const double &x, Vector< double > &polys)
Calculate the Jacobi polnomials all in one goe. More...

## Variables

const double eps = 1.0e-15

## ◆ ddlegendre()

 double oomph::Orthpoly::ddlegendre ( const unsigned & p, const double & x )
inline

Calculates second derivative of Legendre polynomial of degree p at x using three term recursive formula.

Definition at line 144 of file orthpoly.h.

References i.

## ◆ dlegendre()

 double oomph::Orthpoly::dlegendre ( const unsigned & p, const double & x )
inline

Calculates first derivative of Legendre polynomial of degree p at x using three term recursive formula. .

Definition at line 121 of file orthpoly.h.

## ◆ gl_nodes() [1/2]

 void oomph::Orthpoly::gl_nodes ( const unsigned & Nnode, Vector< double > & x )

Definition at line 105 of file orthpoly.cc.

References dlegendre(), eps, legendre(), and oomph::MathematicalConstants::Pi.

## ◆ gl_nodes() [2/2]

 void oomph::Orthpoly::gl_nodes ( const unsigned & Nnode, Vector< double > & x, Vector< double > & w )

Definition at line 148 of file orthpoly.cc.

References dlegendre(), gl_nodes(), and i.

## ◆ gll_nodes() [1/2]

 void oomph::Orthpoly::gll_nodes ( const unsigned & Nnode, Vector< double > & x )

## ◆ gll_nodes() [2/2]

 void oomph::Orthpoly::gll_nodes ( const unsigned & Nnode, Vector< double > & x, Vector< double > & w )

Definition at line 90 of file orthpoly.cc.

References gll_nodes(), i, and legendre().

## ◆ jacobi() [1/2]

 double oomph::Orthpoly::jacobi ( const int & alpha, const int & beta, const unsigned & p, const double & x )
inline

Calculate the Jacobi polnomials.

Definition at line 168 of file orthpoly.h.

## ◆ jacobi() [2/2]

 void oomph::Orthpoly::jacobi ( const int & alpha, const int & beta, const unsigned & p, const double & x, Vector< double > & polys )
inline

Calculate the Jacobi polnomials all in one goe.

Definition at line 200 of file orthpoly.h.

## ◆ legendre()

 double oomph::Orthpoly::legendre ( const unsigned & p, const double & x )
inline

Calculates Legendre polynomial of degree p at x using the three term recurrence relation .

Definition at line 57 of file orthpoly.h.

## ◆ legendre_vector()

 void oomph::Orthpoly::legendre_vector ( const unsigned & p, const double & x, Vector< double > & polys )
inline

Calculates Legendre polynomial of degree p at x using three term recursive formula. Returns all polynomials up to order p in the vector.

Definition at line 88 of file orthpoly.h.