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Volumn 217, Issue 6, 2010, Pages 2684-2697

Jacobi spectral Galerkin method for the integrated forms of second-order differential equations

Author keywords

Diagonalization process; Jacobi polynomials; Poisson and Helmholtz equations; Spectral Galerkin method

Indexed keywords

BASE FUNCTION; DIAGONALIZATIONS; DIRECT SOLUTION; DIRECT SOLVERS; DIRICHLET BOUNDARY CONDITION; DIRICHLET PROBLEM; DISCRETE SYSTEMS; ELLIPTIC EQUATIONS; GALERKIN FORMULATION; HELMHOLTZ; JACOBI POLYNOMIALS; NUMERICAL RESULTS; POLYNOMIAL BASIS; SECOND ORDERS; SECOND-ORDER DIFFERENTIAL EQUATION; SPECTRAL GALERKIN METHOD; SPECTRAL-GALERKIN; STRUCTURED MATRIXES;

EID: 77958020573     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.08.006     Document Type: Article
Times cited : (12)

References (32)
  • 1
    • 0346838024 scopus 로고    scopus 로고
    • Galerkin spectral method for the vorticity and stream function equations
    • F. Auteri, and L. Quartapelle Galerkin spectral method for the vorticity and stream function equations J. Comput. Phys. 149 1999 306 332
    • (1999) J. Comput. Phys. , vol.149 , pp. 306-332
    • Auteri, F.1    Quartapelle, L.2
  • 5
    • 0032498763 scopus 로고    scopus 로고
    • The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function
    • E.H. Doha The ultraspherical coefficients of the moments of a general-order derivative of an infinitely differentiable function J. Comput. Appl. Math. 89 1998 53 72
    • (1998) J. Comput. Appl. Math. , vol.89 , pp. 53-72
    • Doha, E.H.1
  • 6
    • 0037134397 scopus 로고    scopus 로고
    • On the coefficients of differentiated expansions and derivatives of Jacobi polynomials
    • E.H. Doha On the coefficients of differentiated expansions and derivatives of Jacobi polynomials J. Phys. A: Math. Gen. 35 2002 3467 3478
    • (2002) J. Phys. A: Math. Gen. , vol.35 , pp. 3467-3478
    • Doha, E.H.1
  • 7
    • 0037082968 scopus 로고    scopus 로고
    • On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations
    • E.H. Doha On the coefficients of integrated expansions and integrals of ultraspherical polynomials and their applications for solving differential equations J. Comput. Appl. Math. 139 2002 275 298
    • (2002) J. Comput. Appl. Math. , vol.139 , pp. 275-298
    • Doha, E.H.1
  • 8
    • 0037303151 scopus 로고    scopus 로고
    • Explicit formulae for the coefficients of integrated expansions for Jacobi polynomials and their integrals
    • E.H. Doha Explicit formulae for the coefficients of integrated expansions for Jacobi polynomials and their integrals Integr. Transf. Spec. F. 14 1 2003 69 86
    • (2003) Integr. Transf. Spec. F. , vol.14 , Issue.1 , pp. 69-86
    • Doha, E.H.1
  • 9
    • 0742271179 scopus 로고    scopus 로고
    • On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials
    • E.H. Doha On the construction of recurrence relations for the expansion and connection coefficients in series of Jacobi polynomials J. Phys. A: Math. Gen. 37 2004 657 675
    • (2004) J. Phys. A: Math. Gen. , vol.37 , pp. 657-675
    • Doha, E.H.1
  • 10
    • 33747889876 scopus 로고    scopus 로고
    • Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials
    • E.H. Doha, and A.H. Bhrawy Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials Numer. Algorithms 42 2006 137 164
    • (2006) Numer. Algorithms , vol.42 , pp. 137-164
    • Doha, E.H.1    Bhrawy, A.H.2
  • 11
    • 36348973368 scopus 로고    scopus 로고
    • Efficient spectral-Galerkin algorithms for direct solution of the integrated forms for second-order equations using ultraspherical polynomials
    • E.H. Doha, and A.H. Bhrawy Efficient spectral-Galerkin algorithms for direct solution of the integrated forms for second-order equations using ultraspherical polynomials ANZIAM J. 48 2007 361 386
    • (2007) ANZIAM J. , vol.48 , pp. 361-386
    • Doha, E.H.1    Bhrawy, A.H.2
  • 12
    • 44149096688 scopus 로고    scopus 로고
    • Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials
    • E.H. Doha, and A.H. Bhrawy Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials Appl. Numer. Math. 58 2008 1224 1244
    • (2008) Appl. Numer. Math. , vol.58 , pp. 1224-1244
    • Doha, E.H.1    Bhrawy, A.H.2
  • 13
    • 66049087571 scopus 로고    scopus 로고
    • Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations
    • E.H. Doha, and A.H. Bhrawy Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations Numer. Methods PDEs. 25 2009 712 739
    • (2009) Numer. Methods PDEs. , vol.25 , pp. 712-739
    • Doha, E.H.1    Bhrawy, A.H.2
  • 14
    • 61849140746 scopus 로고    scopus 로고
    • Jacobi spectral Galerkin method for elliptic Neumann problems
    • E.H. Doha, A.H. Bhrawy, and W.M. Abd-Elhameed Jacobi spectral Galerkin method for elliptic Neumann problems Numer. Algorithms 50 2009 67 91
    • (2009) Numer. Algorithms , vol.50 , pp. 67-91
    • Doha, E.H.1    Bhrawy, A.H.2    Abd-Elhameed, W.M.3
  • 15
    • 35348984916 scopus 로고    scopus 로고
    • Jacobi Galerkin spectral method for cylindrical and spherical geometries
    • M. Fernandino, C.A. Dorao, and H.A. Jakobsen Jacobi Galerkin spectral method for cylindrical and spherical geometries Chem. Eng. Sci. 62 2007 6777 6783
    • (2007) Chem. Eng. Sci. , vol.62 , pp. 6777-6783
    • Fernandino, M.1    Dorao, C.A.2    Jakobsen, H.A.3
  • 17
    • 0003287471 scopus 로고
    • Polynomial Approximation of Differential Equations
    • Springer-Verlag Heidelberg, Berlin, New York
    • D. Funaro Polynomial Approximation of Differential Equations Lecturer Notes in Physics 1992 Springer-Verlag Heidelberg, Berlin, New York
    • (1992) Lecturer Notes in Physics
    • Funaro, D.1
  • 19
    • 0002665809 scopus 로고    scopus 로고
    • Jacobi spectral approximations to differential equations on the half line
    • B.-Y. Guo Jacobi spectral approximations to differential equations on the half line J. Comp. Math. 18 2000 95 112
    • (2000) J. Comp. Math. , vol.18 , pp. 95-112
    • Guo, B.-Y.1
  • 20
    • 0042825225 scopus 로고    scopus 로고
    • Jacobi spectral method for differential equations with rough asymptotic behaviors at infinity
    • B.-Y. Guo Jacobi spectral method for differential equations with rough asymptotic behaviors at infinity Comput. Math. Appl. 46 2003 95 104
    • (2003) Comput. Math. Appl. , vol.46 , pp. 95-104
    • Guo, B.-Y.1
  • 21
    • 49249143705 scopus 로고
    • The accurate solution of poisson's equation by expansion in Chebyshev polynomials
    • D.B. Haidvogel, and T. Zang The accurate solution of poisson's equation by expansion in Chebyshev polynomials J. Comput. Phys. 30 1979 167 180
    • (1979) J. Comput. Phys. , vol.30 , pp. 167-180
    • Haidvogel, D.B.1    Zang, T.2
  • 22
    • 84968475596 scopus 로고
    • Improved condition number of spectral methods
    • W. Heinrichs Improved condition number of spectral methods Math. comput. 53 1989 103 119
    • (1989) Math. Comput. , vol.53 , pp. 103-119
    • Heinrichs, W.1
  • 23
    • 0012866112 scopus 로고
    • Spectral methods with sparse matrices
    • W. Heinrichs Spectral methods with sparse matrices Numer. Math. 56 1989 25 41
    • (1989) Numer. Math. , vol.56 , pp. 25-41
    • Heinrichs, W.1
  • 26
    • 0025448724 scopus 로고
    • On the coefficients of integrated expansions of ultraspherical polynomials
    • T.N. Phillips, and A. Karageoghis On the coefficients of integrated expansions of ultraspherical polynomials SIAM J. Numer. Anal. 27 1990 823 830
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 823-830
    • Phillips, T.N.1    Karageoghis, A.2
  • 27
    • 0000567049 scopus 로고
    • Efficient spectral-Galerkin method I: Direct solvers of second-and fourth-order equations using Legendre polynomials
    • J. Shen Efficient spectral-Galerkin method I: Direct solvers of second-and fourth-order equations using Legendre polynomials SIAM J. Sci. Comput. 15 1994 1489 1505
    • (1994) SIAM J. Sci. Comput. , vol.15 , pp. 1489-1505
    • Shen, J.1
  • 28
    • 0002543392 scopus 로고
    • Efficient spectral-Galerkin method II: Direct solvers of second-and fourth-order equations using Chebyshev polynomials
    • J. Shen Efficient spectral-Galerkin method II: Direct solvers of second-and fourth-order equations using Chebyshev polynomials SIAM J. Sci. Comput. 16 1995 74 87
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 74-87
    • Shen, J.1
  • 29
    • 0002043336 scopus 로고    scopus 로고
    • Efficient Chebyshev Legendre Galerkin methods for elliptic problems
    • A.V. Ilin and R. Scott, eds Houston J. Math
    • J. Shen, Efficient Chebyshev Legendre Galerkin methods for elliptic problems, in: A.V. Ilin and R. Scott, eds., Proceedings of ICOSAHOM'95, Houston J. Math., 1996, pp. 233-240.
    • (1996) Proceedings of ICOSAHOM'95 , pp. 233-240
    • Shen, J.1
  • 32
    • 0012740492 scopus 로고
    • A note on generalized hypergeometric series
    • (Records for 8 Nov. 1923)
    • G.N. Watson, A note on generalized hypergeometric series, in: Proceedings on London Math. Soc., (2), 23, xiii-xv, 1925, (Records for 8 Nov. 1923).
    • (1925) Proceedings on London Math. Soc. , vol.2 , Issue.23
    • Watson, G.N.1


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