N11 - ME – 510 NUMERICAL METHODS FOR ME II CHEBYSHEV POLYNOMIALS T0(x 1 T1(x x T2(x 2 x 2 1 T3(x 4 x 3 3 x T4(x 8 x 4 8 x 2  1 Tn  1(x 2 x Tn(x

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Unformatted text preview: ME – 510 NUMERICAL METHODS FOR ME II CHEBYSHEV POLYNOMIALS T0 (x) 1 T1 (x) x T2 (x) 2 x 2 - 1 T3 (x) 4 x 3 - 3 x T4 (x) 8 x 4 - 8 x 2  1 Tn  1 (x) 2 x Tn (x) - Tn - 1 (x) 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II CHEBYSHEV POLYNOMIALS ­ ° 1 Tn (x) Tm (x) ° dx ® ³ 1- x2 1 ° ° ¯ 0 Orthogonality Property: S S 2 nzm nm0 n mz0 f (x) a0 f  ¦ a i Ti (x) 2 i1 where ai 2 1 S ³ -1 f (x) Ti (x) 1- x2 dx 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II 1,0 T0=1 T1=x T4 =8x4-8x+1 T2=2 x2-1 0,5 0,0 T3=4 x3-3x 0,5- T5 1,00,0 0,2 0,4 0,6 0,8 1,0 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II 3URI 'U )DUXN $UÕQo Fall 2007 ...
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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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