N21 - ME – 510 NUMERICAL METHODS FOR ME II GAUSS...

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Unformatted text preview: ME – 510 NUMERICAL METHODS FOR ME II GAUSS QUADRATURE METHODS Name Gauss-Legendre Quadrature Formula 1 ³ f (x) dx -1 1 i1 ¦ w i f (x i ) ¦ w i f (x i ) N N Gauss-Chebyshev ³ 1 1- x2 f (x) dx -1 i1 f Gauss-Laguerre -x ³ e f (x) dx 0 i1 ¦ w i f (x i ) N f Gauss-Hermite -x ³ e f (x) dx 2 ¦w i 1 N i f (x i ) -f 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II GAUSS QUADRATURE METHODS Name N 2 Gauss-Legendre 3 4 r xi 0.577350269 0 0.774596669 0.339981043 0.861136312 Nodes and Weights wi 1.00000000 0.888888889 0.555555556 0.652145155 0.347854845 Gauss-Chebyshev xi §1 ¨icos ¨ 2 ¨N ¨ © · ¸ S¸ ¸ ¸ ¹ i 1, 2, ... N wi = S N for all i 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II 2 0.58578 64376 3.41421 35624 0.41577 45568 2.29428 03603 6.28994 50829 0.32254 76896 1.74576 11012 4.53662 02969 9.39507 09123 0.85355 33906 0.14644 66094 0.71109 30099 0.27851 77336 0.01038 92565 0.60315 41043 0.35741 86924 0.03888 79085 0.00053 92947 3 Gauss-Laguerre 4 2 3 0.70710 67811 0. 1.22474 48714 0.52464 76233 1.65068 01239 0. 0.95857 24646 2.02018 28705 0.88622 69255 1.18163 59006 0.29540 89752 0.80491 40900 0.08131 28354 0.94530 87205 0.39361 93232 0.01995 32421 Fall 2007 Gauss-Hermite 4 5 3URI 'U )DUXN $UÕQo ...
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This note was uploaded on 02/28/2011 for the course ME 510 taught by Professor Dr.faruckarinc during the Spring '11 term at Middle East Technical University.

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N21 - ME – 510 NUMERICAL METHODS FOR ME II GAUSS...

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