数据集目录，其中 包含区间 [-1，+1] 的高斯-勒让德正交规则.rar

22 January 2009 9:24:12.580 AM INT_EXACTNESS_LEGENDRE FORTRAN90 version Investigate the polynomial exactness of a Gauss-Legendre quadrature rule by integrating weighted monomials up to a given degree over the [-1,+1] interval. INT_EXACTNESS_LEGENDRE: User input: Quadrature rule X file = "leg_o32_x.txt". Quadrature rule W file = "leg_o32_w.txt". Quadrature rule R file = "leg_o32_r.txt". Maximum degree to check = 70 Spatial dimension = 1 Number of points = 32 The quadrature rule to be tested is a Gauss-Legendre rule ORDER = 32 Standard rule: Integral ( -1 <= x <= +1 ) f(x) dx is to be approximated by sum ( 1 <= I <= ORDER ) w(i) * f(x(i)). Weights W: w( 1) = 0.7018610009470076E-02 w( 2) = 0.1627439473090562E-01 w( 3) = 0.2539206530926209E-01 w( 4) = 0.3427386291302146E-01 w( 5) = 0.4283589802222672E-01 w( 6) = 0.5099805926237620E-01 w( 7) = 0.5868409347853559E-01 w( 8) = 0.6582222277636185E-01 w( 9) = 0.7234579410884846E-01 w(10) = 0.7819389578707038E-01 w(11) = 0.8331192422694680E-01 w(12) = 0.8765209300440382E-01 w(13) = 0.9117387869576392E-01 w(14) = 0.9384439908080459E-01 w(15) = 0.9563872007927485E-01 w(16) = 0.9654008851472773E-01 w(17) = 0.9654008851472773E-01 w(18) = 0.9563872007927485E-01 w(19) = 0.9384439908080459E-01 w(20) = 0.9117387869576392E-01 w(21) = 0.8765209300440382E-01 w(22) = 0.8331192422694680E-01 w(23) = 0.7819389578707038E-01 w(24) = 0.7234579410884846E-01 w(25) = 0.6582222277636185E-01 w(26) = 0.5868409347853559E-01 w(27) = 0.5099805926237620E-01 w(28) = 0.4283589802222672E-01 w(29) = 0.3427386291302146E-01 w(30) = 0.2539206530926209E-01 w(31) = 0.1627439473090562E-01 w(32) = 0.7018610009470076E-02 Abscissas X: x( 1) = -0.9972638618494816 x( 2) = -0.9856115115452684 x( 3) = -0.9647622555875064 x( 4) = -0.9349060759377396 x( 5) = -0.8963211557660521 x( 6) = -0.8493676137325700 x( 7) = -0.7944837959679424 x( 8) = -0.7321821187402897 x( 9) = -0.6630442669302152 x(10) = -0.5877157572407623 x(11) = -0.5068999089322294 x(12) = -0.4213512761306353 x(13) = -0.3318686022821277 x(14) = -0.2392873622521371 x(15) = -0.1444719615827965 x(16) = -0.4830766568773832E-01 x(17) = 0.4830766568773832E-01 x(18) = 0.1444719615827965 x(19) = 0.2392873622521371 x(20) = 0.3318686022821277 x(21) = 0.4213512761306353 x(22) = 0.5068999089322294 x(23) = 0.5877157572407623 x(24) = 0.6630442669302152 x(25) = 0.7321821187402897 x(26) = 0.7944837959679424 x(27) = 0.8493676137325700 x(28) = 0.8963211557660521 x(29) = 0.9349060759377396 x(30) = 0.9647622555875064 x(31) = 0.9856115115452684 x(32) = 0.9972638618494816 Region R: r( 1) = -1.0000000000000000 r( 2) = 1.0000000000000000 A Gauss-Legendre rule would be able to exactly integrate monomials up to and including degree = 63 Error Error Degree (This rule) (Trapezoid) 0.0000000000000002 0.0000000000000007 0 0.0000000000000000 0.0000000000000000 1 0.0000000000000005 0.0020811654526534 2 0.0000000000000000 0.0000000000000000 3 0.0000000000000003 0.0069343306757508 4 0.0000000000000000 0.0000000000000000 5 0.0000000000000000 0.0145479576889774 6 0.0000000000000000 0.0000000000000000 7 0.0000000000000000 0.0249013645725746 8 0.0000000000000000 0.0000000000000000 9 0.0000000000000008 0.0379649165674276 10 0.0000000000000000 0.0000000000000000 11 0.0000000000000004 0.0537003227592496 12 0.0000000000000000 0.0000000000000000 13 0.0000000000000006 0.0720610326999966 14 0.0000000000000000 0.0000000000000000 15 0.0000000000000012 0.0929927250210327 16 0.0000000000000000 0.0000000000000000 17 0.0000000000000012 0.1164338780474923 18 0.0000000000000000 0.0000000000000000 19 0.0000000000000012 0.1423164107074637 20 0.0000000000000000 0.0000000000000000 21 0.0000000000000013 0.1705663807030582 22 0.0000000000000000 0.0000000000000000 23 0.0000000000000014 0.2011047260139807 24 0.0000000000000000 0.0000000000000000 25 0.0000000000000013 0.2338480353580084 26 0.0000000000000000 0.0000000000000000 27 0.0000000000000016 0.2687093332352049 28 0.0000000000000000 0.0000000000000000 29 0.0000000000000017 0.3055988656118886 30 0.0000000000000000 0.0000000000000000 31 0.0000000000000019 0.3444248731157842 32 0.0000000000000000 0.0000000000000000 33 0.0000000000000018 0.3850943397601583 34 0.0000000000000000 0.0000000000000000 35 0.0000000000000018 0.4275137066254632 36 0.0000000000000000 0.0000000000000000 37 0.0000000000000018 0.4715895415292622 38 0.0000000000000000 0.0000000000000000 39 0.0000000000000024 0.5172291574339197 40 0.0000000000000000 0.0000000000000000 41 0.0000000000000019 0.5643411741039599 42 0.0000000000000000 0.0000000000000000 43 0.0000000000000020 0.6128360192641564 44 0.0000000000000000 0.0000000000000000 45 0.0000000000000018 0.6626263671670171 46 0.0000000000000000 0.0000000000000000 47 0.0000000000000017 0.7136275140066652 48 0.0000000000000000 0.0000000000000000 49 0.0000000000000018 0.7657576909791265 50 0.0000000000000000 0.0000000000000000 51 0.0000000000000018 0.8189383169625342 52 0.0000000000000000 0.0000000000000000 53 0.0000000000000017 0.8730941937616883 54 0.0000000000000000 0.0000000000000000 55 0.0000000000000020 0.9281536476270072 56 0.0000000000000000 0.0000000000000000 57 0.0000000000000018 0.9840486213239475 58 0.0000000000000000 0.0000000000000000 59 0.0000000000000019 1.0407147214079759 60 0.0000000000000000 0.0000000000000000 61 0.0000000000000015 1.0980912255700852 62 0.0000000000000000 0.0000000000000000 63 0.0000000000000019 1.1561210549793588 64 0.0000000000000000 0.0000000000000000 65 0.0000000000000020 1.2147507164853362 66 0.0000000000000000 0.0000000000000000 67 0.0000000000000025 1.2739302193767268 68 0.0000000000000000 0.0000000000000000 69 0.0000000000000067 1.3336129711471552 70 INT_EXACTNESS_LEGENDRE: Normal end of execution. 22 January 2009 9:24:12.589 AM