naginterfaces.library.ode.bvp_​ps_​lin_​coeffs

naginterfaces.library.ode.bvp_ps_lin_coeffs(f)[source]

bvp_ps_lin_coeffs obtains the Chebyshev coefficients of a function discretized on Chebyshev Gauss–Lobatto points. The set of discretization points on which the function is evaluated is usually obtained by a previous call to bvp_ps_lin_cgl_grid().

For full information please refer to the NAG Library document for d02ua

https://www.nag.com/numeric/nl/nagdoc_28.5/flhtml/d02/d02uaf.html

Parameters
ffloat, array-like, shape

The function values , for .

Returns
cfloat, ndarray, shape

The Chebyshev coefficients, , for .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: is even.

Notes

bvp_ps_lin_coeffs computes the coefficients , for , of the interpolating Chebyshev series

which interpolates the function evaluated at the Chebyshev Gauss–Lobatto points

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.

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