naginterfaces.library.ode.bvp_​ps_​lin_​cheb_​eval

naginterfaces.library.ode.bvp_ps_lin_cheb_eval(k, x)

bvp_ps_lin_cheb_eval returns the value of the $k$th Chebyshev polynomial evaluated at a point $x\in [-1,1]$. bvp_ps_lin_cheb_eval is primarily a utility function for use by the Chebyshev boundary value problem solvers.

For full information please refer to the NAG Library document for d02uz

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/d02/d02uzf.html

Parameters

kint

The order of the Chebyshev polynomial.

xfloat

The point at which to evaluate the polynomial.

Returns

tfloat

The value, $T$, of the Chebyshev polynomial order $k$ evaluated at $x$.

Raises

NagValueError

(errno $1$)

On entry, $k=⟨value⟩$.

Constraint: $k\ge 0$.

(errno $2$)

On entry, $x=⟨value⟩$.

Constraint: $-1.0\le x\le 1.0$.

Notes

bvp_ps_lin_cheb_eval returns the value, $T$, of the $k$th Chebyshev polynomial evaluated at a point $x\in [-1,1]$; that is, $T=\cos (k\times \arccos \left(x\right))$.

References

Trefethen, L N, 2000, Spectral Methods in MATLAB, SIAM