References
- Al-kholi F.M.R. The coefficients of differentiated expansions of double and triple Chebyshev and Legendre polynomials and their uses for finding the semi-analytical solutions for partial differential equations M.Sc., Thesis Girl' College of Education Jeddah, , Saudi Arabia 1994
- Bellman , R. and Cooke , K.L. 1963 . Differential-Difference Equations , New York : Academic Press .
- 1988 . Spectral Methods in Fluid Dynamics , Berlin : Springer Verlag .
- Dew , P.M. and Scraton , R.E. 1975 . Chebyshev methods for the numerical solution of parabolic partial differential equations in two and three space variables . J.Inst.Maths.Applics. , 16 : 121 – 131 .
- Doha , E.H. 1990a . An Accurate Double Chebyshev Spectral Approximation for Poisson' Equation . Annales Univ.Sci.Budapest, Sect.Comp. , 10 : 243 – 276 .
- Doha , E.H. 1990b . An accurate solution of parabolic equations by expansion in ultraspherical polynomials . Computers Math.Applic. , 19 ( 4 ) : 75 – 88 .
- Doha , E.H. 1991 . The coefficients of differentiated expansions and derivatives of ultraspherical polynomials . Computers Math.Applic. , 21 ( 2-3 ) : 115 – 122 .
- Doha , E.H. 1992 . The Chebyshev Coefficients of General-order Derivatives of an Infinitely Differentiable Function in Two or Three Variables . Annales Univ.Sci.Budapest, Sect.Comp. , 13 : 83 – 91 .
- Doha , E.H. 1995 . On the Coefficients of Differentiated Expansions of Double and Triple Legendre Polynomials . Annales Univ.Sci.Budapest, Sect.Comp. , 15 : 25 – 35 .
- Doha , E.H. 2000 . The Coefficients of Differentiated Expansions of Double and Triple Ultraspherical Polynomials . Annales Univ.Sci.Budapest, Sect.Comp. , 19 : 57 – 79 .
- Doha , E.H. and Helal , M.A. 1997 . An accurate double Chebyshev spectral approximation for parabolic partial differential equations . J.Egypt.Math.Soc. , 5 ( 1 ) : 83 – 101 .
- Fairweather , G. 1978 . Finite Element Galerkin Methods for Differential Equations , New York : Marcel Dekker .
- Gottlieb , D. and Orszag , S.A. . CBMS-NSF Regional Conference Series in Applied Maths. . Numerical Analysis of Spectral Methods: Theory and Applications . Vol. 26 , Philadelphia, PA : SIAM .
- Graham , A. 1981 . Kronecker Product and Matrix Calculus with Applications , London : Ellis Horwood Ltd. .
- Haidvogel , D.B. and Zang , T. 1979 . The accurate solution of Poisson' equation by Chebyshev polynomials . J.Comput.Phys. , 30 : 167 – 180 .
- Horner , T.S. 1982 . “ A double Chebyshev series method for elliptic partial differential equations ” . In Numerical Solution of Partial Differential Equations , Edited by: Noye , J. North-Holland pub.comp. .
- Karageorghis , A. 1988 . A note on the Chebyshev coefficients of the general order derivative of an infinitely differentiable function . J.Comput.Appl.Math. , 21 : 129 – 132 .
- Knibb , D. and Scraton , R.E. 1971 . On the solution of parabolic partial differential equation in Chebyshev series . Comp.J. , 14 : 428 – 432 .
- Lanczos , C. 1957 . Applied Analysis , London : Pitman .
- Loan , C.V. 1992 . Computational Frameworks for Fast Fourier Transform , Philadelphia, , USA : SIAM .
- Luke , Y.L. 1969 . The Special Functions and Their Approximations , Vol. 1 and 2 , New York : Academic Press .
- Orszag , S.A. 1971 . Accurate solution of the orr-Sommer field stability equation . J.Fluid Mech. , 50 : 689 – 703 .
- Phillips , T.N. 1988 . On the Legendre coefficients of a general order derivative of an infinitely differentiable function . IMA J.Numer Anal. , 8 : 455 – 459 .
- Schlichting , H. 1979 . Boundary-Layer Theory , New York : McGraw-Hill .
- 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 .
- Varga , R.S. 1962 . Matrix Iterative Analysis , Englewood Cliffs, N.J : Prentice-Hall, Inc. .