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Volumn 24, Issue 1, 2003, Pages 143-160

Accuracy, resolution, and stability properties of a modified Chebyshev method

Author keywords

Accuracy; Chebyshev collocation; Partial differential equations; Stability

Indexed keywords

COMPUTER SIMULATION; ERROR ANALYSIS; FUNCTIONS; GALERKIN METHODS; PARAMETER ESTIMATION; PARTIAL DIFFERENTIAL EQUATIONS; POLYNOMIALS; PROBLEM SOLVING;

EID: 0037249882     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827500381501     Document Type: Article
Times cited : (21)

References (21)
  • 2
    • 0001096265 scopus 로고
    • Roundoff error in computing derivatives using the Chebyshev differentiation matrix
    • A. Bayliss, A. Class, and B. Matkowsky, Roundoff error in computing derivatives using the Chebyshev differentiation matrix, J. Comput. Phys., 116 (1994), pp. 380-383.
    • (1994) J. Comput. Phys. , vol.116 , pp. 380-383
    • Bayliss, A.1    Class, A.2    Matkowsky, B.3
  • 3
    • 28144442068 scopus 로고
    • Mappings and accuracy for Chebyshev pseudo-spectral approximations
    • A. Bayliss and A. Turkel, Mappings and accuracy for Chebyshev pseudo-spectral approximations, J. Comput. Phys., 101 (1992), pp. 349-359.
    • (1992) J. Comput. Phys. , vol.101 , pp. 349-359
    • Bayliss, A.1    Turkel, A.2
  • 5
    • 0030295512 scopus 로고    scopus 로고
    • Spectral methods on arbitrary grids
    • M.H. Carpenter and D. Gottlieb, Spectral methods on arbitrary grids, J. Comput. Phys., 129 (1996), pp. 74-86.
    • (1996) J. Comput. Phys. , vol.129 , pp. 74-86
    • Carpenter, M.H.1    Gottlieb, D.2
  • 6
    • 0001186440 scopus 로고
    • The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A study of the boundary error
    • M.H. Carpenter, D. Gottlieb, S. Abarbanel, and W.-S. Don, The theoretical accuracy of Runge-Kutta time discretizations for the initial boundary value problem: A study of the boundary error, SIAM J. Sci. Comput., 16 (1995), pp. 1241-1252.
    • (1995) SIAM J. Sci. Comput. , vol.16 , pp. 1241-1252
    • Carpenter, M.H.1    Gottlieb, D.2    Abarbanel, S.3    Don, W.-S.4
  • 7
    • 0031173530 scopus 로고    scopus 로고
    • Accuracy enhancement for higher derivatives using Chebyshev collocation and a mapping technique
    • W.S. Don and A. Solomonoff, Accuracy enhancement for higher derivatives using Chebyshev collocation and a mapping technique, SIAM J. Sci. Comput., 18 (1997), pp. 1040-1055.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 1040-1055
    • Don, W.S.1    Solomonoff, A.2
  • 11
    • 0001374260 scopus 로고    scopus 로고
    • Spectral collocation time-domain modelling of diffractive optical elements
    • J.S. Hesthaven, P.G. Dinesen, and J.P. Lynov, Spectral collocation time-domain modelling of diffractive optical elements, J. Comput. Phys., 155 (1999), pp. 287-306.
    • (1999) J. Comput. Phys. , vol.155 , pp. 287-306
    • Hesthaven, J.S.1    Dinesen, P.G.2    Lynov, J.P.3
  • 15
    • 0030584598 scopus 로고    scopus 로고
    • A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions
    • R. Renaut and J. Frohlich, A pseudospectral Chebychev method for the 2D wave equation with domain stretching and absorbing boundary conditions, J. Comput. Phys., 124 (1996), pp. 324-336.
    • (1996) J. Comput. Phys. , vol.124 , pp. 324-336
    • Renaut, R.1    Frohlich, J.2
  • 16
    • 0043234049 scopus 로고    scopus 로고
    • Evaluation of Chebychev pseudospectral methods for third order differential equations
    • R.A. Renaut and Y. Su, Evaluation of Chebychev pseudospectral methods for third order differential equations, Numer. Algorithms, 16 (1997), pp. 255-281.
    • (1997) Numer. Algorithms , vol.16 , pp. 255-281
    • Renaut, R.A.1    Su, Y.2
  • 17
    • 0031373157 scopus 로고    scopus 로고
    • Stability of a Chebychev pseudospectral solution of the wave equation with absorbing boundaries
    • R. Renaut, Stability of a Chebychev pseudospectral solution of the wave equation with absorbing boundaries, J. Comput. Appl. Math., 87 (1997), pp. 243-259.
    • (1997) J. Comput. Appl. Math. , vol.87 , pp. 243-259
    • Renaut, R.1
  • 18
    • 0029380030 scopus 로고
    • Computational aeroacoustics: Issues and methods
    • C.K.W. Tam, Computational aeroacoustics: Issues and methods, AIAA J., 33 (1995), pp. 1788-1795.
    • (1995) AIAA J. , vol.33 , pp. 1788-1795
    • Tam, C.K.W.1
  • 20
    • 0001399844 scopus 로고
    • The eigenvalues of second-order spectral differentiation matrices
    • J.A.C. Weideman and L.N. Trefethen, The eigenvalues of second-order spectral differentiation matrices, SIAM J. Numer. Anal., 25 (1998), pp. 1279-1298.
    • (1988) SIAM J. Numer. Anal. , vol.25 , pp. 1279-1298
    • Weideman, J.A.C.1    Trefethen, L.N.2
  • 21
    • 0001216115 scopus 로고    scopus 로고
    • Generation of pseudospectral differentiation matrices I
    • B.D. Welfert, Generation of pseudospectral differentiation matrices I, SIAM J. Numer. Anal., 34 (1997), pp. 1640-1657.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1640-1657
    • Welfert, B.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.