Namespaces | Functions | Variables
orthpoly.h File Reference

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Namespaces

 oomph
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 oomph::Orthpoly
 

Functions

double oomph::Orthpoly::legendre (const unsigned &p, const double &x)
 Calculates Legendre polynomial of degree p at x using the three term recurrence relation $ (n+1) P_{n+1} = (2n+1)xP_{n} - nP_{n-1} $. More...
 
void oomph::Orthpoly::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 oomph::Orthpoly::dlegendre (const unsigned &p, const double &x)
 Calculates first derivative of Legendre polynomial of degree p at x using three term recursive formula. $ nP_{n+1}^{'} = (2n+1)xP_{n}^{'} - (n+1)P_{n-1}^{'} $. More...
 
double oomph::Orthpoly::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 oomph::Orthpoly::jacobi (const int &alpha, const int &beta, const unsigned &p, const double &x)
 Calculate the Jacobi polnomials. More...
 
void oomph::Orthpoly::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...
 
void oomph::Orthpoly::gll_nodes (const unsigned &Nnode, Vector< double > &x)
 Calculates the Gauss Lobatto Legendre abscissas for degree p = NNode-1. More...
 
void oomph::Orthpoly::gll_nodes (const unsigned &Nnode, Vector< double > &x, Vector< double > &w)
 
void oomph::Orthpoly::gl_nodes (const unsigned &Nnode, Vector< double > &x)
 
void oomph::Orthpoly::gl_nodes (const unsigned &Nnode, Vector< double > &x, Vector< double > &w)
 

Variables

const double oomph::Orthpoly::eps = 1.0e-15