naginterfaces.library.ode.bvp_ps_lin_cgl_grid¶

naginterfaces.library.ode.bvp_ps_lin_cgl_grid(n, a, b)[source]¶

bvp_ps_lin_cgl_grid returns the Chebyshev Gauss–Lobatto grid points on $[a, b]$ .

For full information please refer to the NAG Library document for d02uc

Parameters

nint: $n$ , where the number of grid points is $n + 1$ . This is also the largest order of Chebyshev polynomial in the Chebyshev series to be computed.
afloat: $a$ , the lower bound of domain $[a, b]$ .
bfloat: $b$ , the upper bound of domain $[a, b]$ .

Returns

xfloat, ndarray, shape $(n + 1)$: The Chebyshev Gauss–Lobatto grid points, $x_{i}$ , for $i = 1, 2, \dots, n + 1$ , on $[a, b]$ .

Raises

NagValueError

(errno $1$ )

On entry, $n = ⟨ v a l u e ⟩$ .

Constraint: $n > 0$ .

(errno $1$ )

On entry, $n = ⟨ v a l u e ⟩$ .

Constraint: $n$ is even.

(errno $2$ )

On entry, $a = ⟨ v a l u e ⟩$ and $b = ⟨ v a l u e ⟩$ .

Constraint: $a < b$ .

Notes: bvp_ps_lin_cgl_grid returns the Chebyshev Gauss–Lobatto grid points on $[a, b]$ . The Chebyshev Gauss–Lobatto points on $[- 1, 1]$ are computed as $t_{i} = - cos (\frac{(i - 1) π}{n})$ , for $i = 1, 2, \dots, n + 1$ . The Chebyshev Gauss–Lobatto points on an arbitrary domain $[a, b]$ are:

$x_{i} = \frac{b - a}{2} t_{i} + \frac{a + b}{2}, i = 1, 2, \dots, n + 1 .$

NAG and Python