JACOBI_RULE_SS is a C++ program which generates a specific Gauss-Jacobi quadrature rule, based on user input.
The rule can be output as text in a standard programming language, or the data can be written to three files for easy use as input to other programs.
The Gauss-Jacobi quadrature rule is designed to approximate integrals on the interval [-1,1], with a weight function of the form (1-x)^{ALPHA} * (1+x)^{BETA}. ALPHA and BETA are real parameters that must be greater than -1.
Gauss-Jacobi quadrature assumes that the integrand we are considering has a form like:
Integral ( -1 <= x <= +1 ) (1-x)^alpha (1+x)^beta f(x) dx
The standard Gauss-Jacobi quadrature rule is used as follows:
Integral ( -1 <= x <= +1 ) (1-x)^alpha (1+x)^beta f(x) dxis to be approximated by
Sum ( 1 <= i <= order ) w(i) * f(x(i))
jacobi_rule_ss order alpha beta outputwhere
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
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jacobi_rule_ss 4 0.0 0.0 C++
jacobi_rule_ss 4 1.0 0.0 F77
jacobi_rule_ss 4 0.0 1.0 F90
jacobi_rule_ss 8 1.0 1.0 MAT
jacobi_rule_ss 4 0.5 1.5 jac_o4_a0.5_b1.5
jacobi_rule_ss 4 0.5 1.5 jac_o4_a0.5_b1.5
jacobi_rule_ss 4 0.5 1.5 jac_o4_a0.5_b1.5
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