quad {rjacobi}R Documentation

Gauss-Jacobi Quadrature Parameters

Description

Calculates the Interpolation matrix of the Q point Gauss-Jacobi quadrature.

Usage

quad <- quadGJ(Q, a=0, b=0)
quad <- quadGLJ(Q, a=0, b=0)
quad <- quadGRJM(Q, a=0, b=0)
quad <- quadGRJP(Q, a=0, b=0)

Arguments

Q Number of quadrature points
a α parameter of Jacobi polynomial. Defaults to 0
b β parameter of Jacobi polynomial. Defaults to 0

Details

This function is actually a set of wrappers around the functions zerosGJ, weightsGJ, diffmatGJ and interpmatGJ.

It is basically a friendly interface to these functions.

Different types of quadrature are possible:

Value

x Quadrature nodes
w Quadrature weights
D Derivative matrix
interp A function that computes the interpolation matrix given a set of nodes.

References

Abramowitz, Milton and Stegun, Irene (editors); "Handbook of Mathematical functions", Dover Publications 1965.

Karniadakis, George Em and Sherwin, Spencer; "Spectral/hp Element Methods for Computational Fluid Dynamics", Oxford Science Publications, 2nd edition, 2005.

See Also

quadrature zerosGJ weightsGJ diffmatGJ interpmatGJ

Examples


## Calculates the numerical derivative of jacobi(x,4)
q = quadGJ(5)
f <- jacobi(q$x, 4)
df <- q$D %*% f

x <- seq(-1, 1, len=51)
ff <- djacobi(x, 4)

plot(x, ff, ty='l', xlab="x", ylab="dP_4^(0,0)/dx", main="Analytical and
Numerical derivative")
points(q$x,df)


[Package rjacobi version 0.9.2 Index]