naginterfaces.library.ode.bvp_ps_lin_cgl_vals¶
- naginterfaces.library.ode.bvp_ps_lin_cgl_vals(a, b, q, c)[source]¶
bvp_ps_lin_cgl_vals
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 bybvp_ps_lin_coeffs()
orbvp_ps_lin_solve()
.For full information please refer to the NAG Library document for d02ub
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/d02/d02ubf.html
- Parameters
- afloat
, the lower bound of domain .
- bfloat
, the upper bound of domain .
- qint
The order, , of the derivative to evaluate.
- cfloat, array-like, shape
The Chebyshev coefficients, , for .
- Returns
- ffloat, ndarray, shape
The derivatives , for , of the Chebyshev series, .
- Raises
- NagValueError
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: is even.
- (errno )
On entry, and .
Constraint: .
- (errno )
On entry, .
Constraint: .
- Notes
bvp_ps_lin_cgl_vals
evaluates the Chebyshev seriesor 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).
- References
Canuto, C, 1988, Spectral Methods in Fluid Dynamics, 502, Springer
Canuto, C, Hussaini, M Y, Quarteroni, A and Zang, T A, 2006, Spectral Methods: Fundamentals in Single Domains, Springer
Trefethen, L N, 2000, Spectral Methods in MATLAB, SIAM