Routines For Orthogonal Polynomial Calculus and Interpolation
Spencer Sherwin, Aeronautics, Imperial College London
Based on codes by Einar Ronquist and Ron Henderson
Abbreviations
z - Set of collocation/quadrature points
w - Set of quadrature weights
D - Derivative matrix
h - Lagrange Interpolant
I - Interpolation matrix
g - Gauss
gr - Gauss-Radau
gl - Gauss-Lobatto
j - Jacobi
m - point at minus 1 in Radau rules
p - point at plus 1 in Radau rules
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MAIN ROUTINES
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Points and Weights:
zwgj Compute Gauss-Jacobi points and weights
zwgrjm Compute Gauss-Radau-Jacobi points and weights (z=-1)
zwgrjp Compute Gauss-Radau-Jacobi points and weights (z= 1)
zwglj Compute Gauss-Lobatto-Jacobi points and weights
jacobfd Returns value and derivative of Jacobi poly. at point z
jacobd Returns derivative of Jacobi poly. at point z (valid at z=-1,1)
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LOCAL ROUTINES
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jacobz Returns Jacobi polynomial zeros
gammaf Gamma function for integer values and halves