NAG Library Function Document

nag_ode_bvp_ps_lin_cheb_eval (d02uzc)

1: k – IntegerInput: On entry: the order of the Chebyshev polynomial.
Constraint: $k \geq 0$ .
2: x – doubleInput: On entry: the point at which to evaluate the polynomial.
Constraint: $- 1.0 \leq x \leq 1.0$ .
3: t – double *Output: On exit: the value, $T$ , of the Chebyshev polynomial order $k$ evaluated at $x$ .
4: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_INT: On entry, $k = ⟨value⟩$ .
Constraint: $k \geq 0$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_REAL: On entry, $x = ⟨value⟩$ .
Constraint: $- 1.0 \leq x \leq 1.0$ .

7 Accuracy

The accuracy should be close to machine precision.

8 Parallelism and Performance

Not applicable.

9 Further Comments

None.

10 Example

A set of Chebyshev coefficients is obtained for the function

x + \exp (- x)

defined on

[- 0.24 \times π, 0.5 \times π]

using nag_ode_bvp_ps_lin_cgl_grid (d02ucc). At each of a set of new grid points in the domain of the function nag_ode_bvp_ps_lin_cheb_eval (d02uzc) is used to evaluate each Chebshev polynomial in the series representation. The values obtained are multiplied to the Chebyshev coefficients and summed to obtain approximations to the given function at the new grid points.

NAG Library Function Documentnag_ode_bvp_ps_lin_cheb_eval (d02uzc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG Library Function Document

nag_ode_bvp_ps_lin_cheb_eval (d02uzc)