NAG Library Function Document
nag_ode_bvp_ps_lin_quad_weights (d02uyc)
1
Purpose
nag_ode_bvp_ps_lin_quad_weights (d02uyc) obtains the weights for Clenshaw–Curtis quadrature at Chebyshev points. This allows for fast approximations of integrals for functions specified on Chebyshev Gauss–Lobatto points on .
2
Specification
#include <nag.h> |
#include <nagd02.h> |
void |
nag_ode_bvp_ps_lin_quad_weights (Integer n,
double w[],
NagError *fail) |
|
3
Description
nag_ode_bvp_ps_lin_quad_weights (d02uyc) obtains the weights for Clenshaw–Curtis quadrature at Chebyshev points.
Given the (Clenshaw–Curtis) weights , for , and function values (where , for , are the Chebyshev Gauss–Lobatto points), then .
For a function discretized on a Chebyshev Gauss–Lobatto grid on the resultant summation must be multiplied by the factor .
4
References
Trefethen L N (2000) Spectral Methods in MATLAB SIAM
5
Arguments
- 1:
– IntegerInput
-
On entry: , where the number of grid points is .
Constraint:
and
n is even.
- 2:
– doubleOutput
-
On exit: the Clenshaw–Curtis quadrature weights,
, for .
- 3:
– NagError *Input/Output
-
The NAG error argument (see
Section 3.7 in How to Use the NAG Library and its Documentation).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_INT
-
On entry, .
Constraint: .
On entry,
.
Constraint:
n is even.
- 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.
See
Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
7
Accuracy
The accuracy should be close to machine precision.
8
Parallelism and Performance
nag_ode_bvp_ps_lin_quad_weights (d02uyc) is not threaded in any implementation.
A real array of length is internally allocated.
10
Example
This example approximates the integral using Clenshaw–Curtis weights and a -point Chebyshev Gauss–Lobatto grid on .
10.1
Program Text
Program Text (d02uyce.c)
10.2
Program Data
Program Data (d02uyce.d)
10.3
Program Results
Program Results (d02uyce.r)