nag_ode_bvp_ps_lin_cgl_vals (d02ubc) evaluates a function, or one of its lower order derivatives, from its Chebyshev series representation at Chebyshev Gauss–Lobatto points on
. The coefficients of the Chebyshev series representation required are usually derived from those returned by
nag_ode_bvp_ps_lin_coeffs (d02uac) or
nag_ode_bvp_ps_lin_solve (d02uec).
nag_ode_bvp_ps_lin_cgl_vals (d02ubc) evaluates the Chebyshev series
or its derivative (up to fourth order) at the Chebyshev Gauss–Lobatto points on
. Here
denotes the Chebyshev polynomial of the first kind of degree
with argument
defined on
. In terms of your original variable,
say, the input values at which the function values are to be provided are
where
and
are respectively the upper and lower ends of the range of
over which the function is required.
The calculation is implemented by a forward one-dimensional discrete Fast Fourier Transform (DFT).
- 1:
n – IntegerInput
On entry: , where the number of grid points is . This is also the largest order of Chebyshev polynomial in the Chebyshev series to be computed.
Constraint:
and
n is even.
- 2:
a – doubleInput
On entry: , the lower bound of domain .
Constraint:
.
- 3:
b – doubleInput
On entry: , the upper bound of domain .
Constraint:
.
- 4:
q – IntegerInput
On entry: the order, , of the derivative to evaluate.
Constraint:
.
- 5:
c[] – const doubleInput
On entry: the Chebyshev coefficients,
, for .
- 6:
f[] – doubleOutput
On exit: the derivatives
, for , of the Chebyshev series, .
- 7:
fail – NagError *Input/Output
-
The NAG error argument (see
Section 3.6 in the Essential Introduction).
nag_ode_bvp_ps_lin_cgl_vals (d02ubc) is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
nag_ode_bvp_ps_lin_cgl_vals (d02ubc) makes calls to BLAS and/or LAPACK routines, which may be threaded within the vendor library used by this implementation. Consult the documentation for the vendor library for further information.
Please consult the
Users' Note for your implementation for any additional implementation-specific information.
See
Section 10 in nag_ode_bvp_ps_lin_solve (d02uec).