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Original Articles

Double ultraspherical solution of eigenvalue problems for partial differential equations

Pages 289-301 | Received 09 May 2000, Published online: 19 Mar 2007

References

  • Brandt , A. , Mc Cormick , S. and Runge , J. 1983 . Multigrid Methods for Differential Eigen-problems . SIAM J.Scientific and Statistical.Comput. , 4 : 244 – 260 .
  • Canuto , C , Hussaini , M.Y. , Quarteroni , A. and Zang , T.A. 1988 . Spectral Methods in Fluid Dynamic , New York : Springer-Verlag .
  • Doha , E.H. 1998 . The Ultraspherical Coefficients of Moments of a General Order Derivatives of an Infinitely Differentiable Function . J.Comput.and Appl.Math. , 89 : 53 – 72 .
  • El-Gendi , S.E. 1969 . Chebyshev Solutions of Differential, Integral, and Integro-Differential Equations . Computer J. , 12 : 282 – 287 .
  • El-Hawary , H.M. , Salim , M.S. and Hussien , H.S. 2000 . An Optimal Ultraspherical Approximation of Integrals . Intern.J.of Computer and Math. , 77 ( 1-2 )
  • El-Hawary , H.M. , Salim , M.S. and Hussien , H.S. 2000 . Legendre Spectral Method for Solving Integral and Integro-Differential Equations . Intern.J.of Computer and Math. , 75 : 187 – 203 .
  • El-Hawary , H.M. 1994 . Double Chebyshev Solution of Eigenvalue Problems for Partial Differential Equations . Intern.J.of Computer Math. , 54 : 197 – 206 .
  • El-Hawary , H.M. 1991 . Numerical Solution of Eigenvalue Problems for Partial Differential Equations . J.of Inst.Math.and Comp.Sci. , 4 ( 2 ) : 241 – 248 .
  • Frankel , J.I. and Osborne , G.E. 1999 . A New Time Treatment for Solving Partial Integro-Differential Equations of Radiative Transport . IMA J.of Numerical Analysis , 19 : 91 – 103 .
  • Gottlib , D. and Orszag , S.A. 1977 . CBMS-NSF Regional Conference Series in Applied Mathematics . Numerical Analysis of Spectral Methods: Theory and Applications . 1977 . Vol. 26 ,
  • Graham , A. 1981 . Kronccker Products and Matrix Calculus with Applications , London : Ellis Horwood .
  • Haidvogel , D.B. and Zang , T. 1979 . The Accurate Solution of Poisson's Equation by Expansion in Chebyshev Polynomials . J.Comput.Physics , 30 : 167 – 180 .
  • Kim , Y.J. , Kwon , K.H. and Lee , J.N. 1998 . Partial Differential Equations Having Orthogonal Polynomial Solutions . J.Comput.and Applied Math. , 99 : 239 – 253 .
  • Liu , K.M. and Ortiz , E.L. 1986 . Numerical Solution of Eigenvalue Problems for Partial Differential Equations with the Tau-Lines Method . Comp.and Maths.with Appls. , 12B : 1153 – 1168 .
  • Siyyam , H.I. and Syam , M.I. 1997 . An Accurate Solution of the Poisson Equation by the Chebyshev-Tau Method . J.Computational and Applied Math. , 85 : 1 – 10 .
  • Szegö . 1985 . Orthogonal Polynomials . Am.Math.Soc.Colloq.Pub. , 23

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