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Original Articles

On the legendre coefficients of the moments of the general order derivative of an infinitely differentiable function

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Pages 107-122 | Received 02 Mar 1994, Published online: 20 Mar 2007

References

  • Boateng , G. K. 1975 . A practical Chebyshev collocation method for differential equations . Intern. J. Computer Maths , 5 : 59 – 79 . Section B
  • Canuto , C. 1988 . Spectral Methods in Fluid Dynamic , Berlin : Springer-Verlag .
  • Cash , J. R. 1978 . An extension of Olver's method for the numerical solution of linear recurrence relations . Math. Comp. , 32 : 497 – 510 .
  • Cash , J. R. 1980a . A note on Olver's algorithm for the solution of second-order linear difference equations . Math. Comp. , 35 : 767 – 772 .
  • Cash , J. R. 1980b . A note, on the numerical solution of linear recurrence relations . Numer. Math. , 34 : 371 – 386 .
  • Doha , E. H. 1990 . An accurate solution of parabolic equations by expansion in ultraspherical poly-nomials . J. Comp. Math. Applic. , 19 : 75 – 88 .
  • Doha , E. H. 1991 . The coefficients of differentiated expansions and derivatives of ultraspherical poly-nomials . J. Comp. Math. Applic. , 21 : 115 – 122 .
  • Doha , E. H. 1994 . The first and second kinds Chebyshev coefficients of the moments of the general order derivative of an infinitely differentiable function . Intern. J. Computer Math. , 51 : 21 – 35 .
  • Fox , L. and Parker , I. B. 1972 . “ Chebyshev Polynomials in Numerical Analysis ” . London : Oxford University Press .
  • Gottlieb , D. and Orszag , S. A. . Numerical Analysis of Spectral Methods: Theory and Applications . CBMS-NSF Regional Conference Series in Applied Maths . 1977 . Philadelphia : SIAM .
  • Horner , T. S. 1980 . Recurrence relations for the coefficients in Chebyshev series solutions of ordinary differential equations . Math. Comp. , 35 ( 151 ) : 893 – 905 .
  • Karageorghis , A. 1988a . Chebyshev spectral methods for solving two-point boundary value problems arising in heat transfer . J. Comput. Methods Appl. Mech. Eng. , 70 ( 151 ) : 103 – 121 .
  • Karageorghis , A. 1988b . A note on the Chebyshev coefficients of the general order derivative of an infinite-ly differentiable function . J. Comput. Appl. Math. , 21 ( 151 ) : 129 – 132 .
  • Karageorghis , A. 1988c . A note on the Chebyshev coefficients of the moments of the general order derivative of an infinitely differentiable function . J. Comput. Appl. Math. , 21 ( 151 ) : 383 – 386 .
  • Karageorghis , A. and Phillips , T. N. 1988 . Spectral Galerkin methods for the primary two-point boundary value problems in modelling viscoelastic flows . Inter. J. Numer. Meth. Engrg. , 26 ( 151 ) : 647 – 662 .
  • Karageorghis , A. and Phillips , T. N. 1989 . Chebyshev spectral collocation methods for laminar flow through a channel contraction . J. Comput. Phys. , 84 ( 151 ) : 114 – 133 .
  • Lewanowicz , S. 1976 . Construction of a recurrence relation of the lowest order for coefficients of the Gegenbauer series . Zastos. Math. , 15 ( 151 ) : 345 – 396 . Applicationes Mathematicae
  • Lewanowicz , S. 1986 . Recurrence relations for the coefficients in Jacobi series solutions of linear differential equations . SIAM J. Math. Anal. , 17 ( 5 ) : 1037 – 1052 .
  • Luke , Y. 1969 . The Special Functions and Their Approximations Vol. 1,2 , New York, London
  • Morris , A. G. and Horner , T. S. 1977 . Chebyshev polynomials in the numerical solution of differential equations . Math. Comp. , 31 ( 140 ) : 881 – 891 .
  • Oliver , J. 1968 . The numerical solution of linear recurrence relations . Numer. Math. , 11 : 349 – 360 .
  • Scraton , R. E. 1972 . A modification of Miller's recurrence algorithm . BIT , 12 : 242 – 251 .
  • 1985 . Spectral multigrid methods with applications to transonic potential flow . J. Comput.Phys. , 57 : 43 – 76 .
  • Tal-Ezer , H. 1986 . A pseudospectral Legendre method for hyperbolic equations with an improved stability condition . J. Comput, Phys. , 67 : 145 – 172 .
  • Voigt , R. G. , ed. 1984 . Spectral Methods for Partial Differential Equations , Philadelphia : SIAM .
  • Wimp , J. 1984 . Computation with Recurrence Relations , London : Pitman Advanced Publising Program .

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