cc_project
cc_project,
an Octave code which
investigates the extension of a Clenshaw-Curtis-like quadrature
scheme to semi-infinite and infinite intervals, and to integrands
with a specified density function.
The Legendre integral for f(x) is:
I(f) = integral ( -1 <= x <= +1 ) f(x) dx
Quadrature rules for the Legendre integral include:
-
Clenshaw-Curtis quadrature, a sequence of nested quadrature rules,
which include the endpoints; the rule of order N has exactness
N-1 (if N is even) or N (if N is odd);
-
Fejer Type 2 quadrature, a sequence of nested quadrature rules,
which include the endpoints; the rule of order N has exactness
N-1 (if N is even) or N (if N is odd);
The Laguerre integral for f(x) is:
I(f) = integral ( 0 <= x <= +oo ) f(x) rho(x) dx
Depending on the value of the density function rho(x) we have:
-
rho(x) = exp(-x): Laguerre 0 integral;
-
rho(x) = 1: Laguerre 1 integral.
Quadrature rules include:
-
CCFI_0 rules for integral ( 0 <= x <= +oo ) f(x) exp(-x) dx;
-
CCFI_1 rules for integral ( 0 <= x <= +oo ) f(x) dx.
Licensing:
The information on this web page is distributed under the MIT license.
Languages:
cc_project is available in
a MATLAB version and
an Octave version.
Related Data and Programs:
cc_project_test
Reference:
-
John Boyd,
Exponentially convergent Fourier-Chebyshev quadrature schemes on
bounded and infinite intervals,
Journal of Scientific Computing,
Volume 2, Number 2, 1987, pages 99-109.
Source Code:
-
cardinal_cos.m,
evaluates a cardinal cosine interpolation basis function.
-
cardinal_sin.m,
evaluates a cardinal sine interpolation basis function.
-
ccff.m,
defines points and weights for Boyd's quadrature rule
for [-1,1] with density 1.
-
ccff_asymptotic.m,
examines asymptotic error for a given integrand,
for Boyd's quadrature rule for [-1,+1]
with density 1.
-
ccfi_0.m,
defines points and weights for Boyd's quadrature rule
for [0,+oo) with density exp(-x).
-
ccfi_1.m,
defines points and weights for Boyd's quadrature rule
for [0,+oo) with density 1.
-
ccii_0.m,
defines points and weights for Boyd's quadrature rule
for (-oo,+oo) with density exp(-x^2).
-
ccii_1.m,
defines points and weights for Boyd's quadrature rule
for (-oo,+oo) with density 1.
-
chebyshev1_compute.m
computes a Gauss-Chebyshev type 1 quadrature rule.
-
chebyshev2_compute.m
computes a Gauss-Chebyshev type 2 quadrature rule.
-
chebyshev3_compute.m,
computes a Gauss-Chebyshev type 3 quadrature rule.
-
fejer1_compute.m,
computes a Fejer type 1 quadrature rule.
-
fejer2_compute.m,
computes a Fejer type 2 quadrature rule.
-
legendre_integral.m,
returns the value of the Legendre integral of a monomial.
-
legendre_monomial_quadrature.m,
determines the error when a quadrature rule is applied to the
Legendre integral of a monomial.
-
legendre_test_integral.m,
returns the exact value of the Legendre integral of the
test integrand.
-
legendre_test_integrand.m,
evaluates a test integrand for the Legendre integral.
-
r8_mop.m,
evaluates an integer power of -1 as an R8.
Last modified on 12 January 2021.