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Volumn 34, Issue 4, 1997, Pages 1451-1471

Spectrally accurate solution of nonperiodic differential equations by the Fourier-Gegenbauer method

Author keywords

Exponential accuracy; Fourier series; Gegenbauer series; Gibbs phenomenon; Green's functions; Helmholtz equation

Indexed keywords


EID: 0000626401     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142994278814     Document Type: Article
Times cited : (14)

References (12)
  • 1
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    • On the Gibbs Phenomenon I: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function
    • D. GOTTLIEB, C.W. SHU, A. SOLOMONOFF, AND H. VANDEVON, On the Gibbs Phenomenon I: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function, J. Comput. Appl. Math., 43 (1992), pp. 81-92.
    • (1992) J. Comput. Appl. Math. , vol.43 , pp. 81-92
    • Gottlieb, D.1    Shu, C.W.2    Solomonoff, A.3    Vandevon, H.4
  • 2
    • 0028446136 scopus 로고
    • Resolution properties of the Fourier method for discontinuous waves
    • D. GOTTLIEB AND C.W. SHU, Resolution properties of the Fourier method for discontinuous waves, Comput. Meth. Appl. Mech. Engrg., 116 (1994), pp. 27-37.
    • (1994) Comput. Meth. Appl. Mech. Engrg. , vol.116 , pp. 27-37
    • Gottlieb, D.1    Shu, C.W.2
  • 3
    • 0347990856 scopus 로고
    • On the Gibbs Phenomenon III: Recovering Exponential Accuracy in a Sub-Interval from the Spectral Partial Sum of a Piecewise Analytic Function
    • D. GOTTLIEB AND C.W. SHU, On the Gibbs Phenomenon III: Recovering Exponential Accuracy in a Sub-Interval from the Spectral Partial Sum of a Piecewise Analytic Function, ICASE Report 93-82, 1993.
    • (1993) ICASE Report , vol.93 , Issue.82
    • Gottlieb, D.1    Shu, C.W.2
  • 4
    • 0001338069 scopus 로고    scopus 로고
    • On the Gibbs Phenomenon V: Recovering exponential accuracy from collocation point values of a piecewise analytic function
    • D. GOTTLIEB AND C.W. SHU, On the Gibbs Phenomenon V: Recovering exponential accuracy from collocation point values of a piecewise analytic function, Numer. Math., 33 (1996), pp. 280-290.
    • (1996) Numer. Math. , vol.33 , pp. 280-290
    • Gottlieb, D.1    Shu, C.W.2
  • 5
    • 0026907997 scopus 로고
    • On one-side filters for spectral Fourier approximations of discontinuous functions
    • W. CAI, D. GOTTLIEB, AND C.W. SHU, On one-side filters for spectral Fourier approximations of discontinuous functions, SIAM J. Numer. Anal., 29 (1992), pp. 905-916.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 905-916
    • Cai, W.1    Gottlieb, D.2    Shu, C.W.3
  • 6
    • 0346099629 scopus 로고
    • The CFL Conditions for Spectral Approximations to Hyperbolic Initial-Boundary Value Problems
    • D. GOTTLIEB AND E. TADMOR, The CFL Conditions for Spectral Approximations to Hyperbolic Initial-Boundary Value Problems, ICASE Report 90-42, 1990.
    • (1990) ICASE Report , vol.90 , Issue.42
    • Gottlieb, D.1    Tadmor, E.2
  • 8
    • 0027617990 scopus 로고
    • A spectral multi-domain technique with local Fourier basis
    • M. ISRAELI, L. VOZOVOI, AND A. AVERBUCH, A spectral multi-domain technique with local Fourier basis, J. Sci. Comput., 8 (1993), pp. 181-185.
    • (1993) J. Sci. Comput. , vol.8 , pp. 181-185
    • Israeli, M.1    Vozovoi, L.2    Averbuch, A.3
  • 9
    • 0347360610 scopus 로고
    • Parallelizing implicit algorithms for evolution equations by domain decomposition
    • M. ISRAELI, L. VOZOVOI, AND A. AVERBUCH, Parallelizing implicit algorithms for evolution equations by domain decomposition, J. Sci. Comput., 8 (1993), pp. 197-212.
    • (1993) J. Sci. Comput. , vol.8 , pp. 197-212
    • Israeli, M.1    Vozovoi, L.2    Averbuch, A.3
  • 10
    • 0005729077 scopus 로고    scopus 로고
    • Analysis and application of Fourier-Gegenbauer method to stiff differential equations
    • L. VOZOVOI, M. ISRAELI, AND A. AVERBUCH, Analysis and application of Fourier-Gegenbauer method to stiff differential equations, SIAM J. Numer. Anal., 33 (1996), pp. 1844-1863.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1844-1863
    • Vozovoi, L.1    Israeli, M.2    Averbuch, A.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.