NAG Library Function Document
nag_ode_bvp_ps_lin_cheb_eval (d02uzc) returns the value of the th Chebyshev polynomial evaluated at a point . nag_ode_bvp_ps_lin_cheb_eval (d02uzc) is primarily a utility function for use by the Chebyshev boundary value problem solvers.
||nag_ode_bvp_ps_lin_cheb_eval (Integer k,
nag_ode_bvp_ps_lin_cheb_eval (d02uzc) returns the value, , of the th Chebyshev polynomial evaluated at a point ; that is, .
Trefethen L N (2000) Spectral Methods in MATLAB SIAM
k – IntegerInput
On entry: the order of the Chebyshev polynomial.
x – doubleInput
On entry: the point at which to evaluate the polynomial.
t – double *Output
On exit: the value, , of the Chebyshev polynomial order evaluated at .
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, argument had an illegal value.
On entry, .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG
On entry, .
The accuracy should be close to machine precision.
8 Parallelism and Performance
A set of Chebyshev coefficients is obtained for the function
using nag_ode_bvp_ps_lin_cgl_grid (d02ucc)
. At each of a set of new grid points in the domain of the function nag_ode_bvp_ps_lin_cheb_eval (d02uzc) is used to evaluate each Chebshev polynomial in the series representation. The values obtained are multiplied to the Chebyshev coefficients and summed to obtain approximations to the given function at the new grid points.
10.1 Program Text
Program Text (d02uzce.c)
10.2 Program Data
Program Data (d02uzce.d)
10.3 Program Results
Program Results (d02uzce.r)