07-Jan-2022 21:57:50 jacobi_exactness_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test jacobi_exactness(). 07-Jan-2022 21:57:50 JACOBI_EXACTNESS MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Investigate the polynomial exactness of a Gauss-Jacobi quadrature rule by integrating weighted monomials up to a given degree over the [-1,+1] interval. JACOBI_EXACTNESS: User input: Quadrature rule X file = "jac_o2_a0.5_b1.5_x.txt". Quadrature rule W file = "jac_o2_a0.5_b1.5_w.txt". Quadrature rule R file = "jac_o2_a0.5_b1.5_r.txt". Maximum degree to check = 5 Exponent of (1-x), ALPHA = 0.500000 Exponent of (1+x), BETA = 1.500000 Spatial dimension = 1 Number of points = 2 The quadrature rule to be tested is a Gauss-Jacobi rule ORDER = 2 ALPHA = 0.500000 BETA = 1.500000 Standard rule: Integral ( -1 <= x <= +1 ) (1-x)^alpha (1+x)^beta f(x) dx is to be approximated by sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). Weights W: w(1) = 0.6369718619318372 w(2) = 0.9338244648627007 Abscissas X: x(1) = -0.2742918851774317 x(2) = 0.6076252185107651 Region R: r(1) = -1.000000e+00 r(2) = 1.000000e+00 A Gauss-Jacobi rule would be able to exactly integrate monomials up to and including degree = 3 Error Degree 0.0000000000002283 0 0.0000000000002284 1 0.0000000000002282 2 0.0000000000002277 3 0.3333333333334854 4 0.3777777777779199 5 JACOBI_EXACTNESS: Normal end of execution. 07-Jan-2022 21:57:50 jacobi_exactness_test(): Normal end of execution. 07-Jan-2022 21:57:50