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 by bvp_ps_lin_coeffs() or bvp_ps_lin_solve().

For full information please refer to the NAG Library document for d02ub

https://www.nag.com/numeric/nl/nagdoc_28.5/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 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).

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