메뉴 건너뛰기




Volumn 201, Issue 1, 2007, Pages 30-47

A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems

Author keywords

Biharmonic problems; Integrated Chebyshev polynomials; Multiple boundary conditions; Spectral collocation methods

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; HARMONIC ANALYSIS; INTEGRATION; POLYNOMIALS; PROBLEM SOLVING;

EID: 33846126316     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.01.030     Document Type: Article
Times cited : (57)

References (28)
  • 2
    • 0001096265 scopus 로고
    • Roundoff error in computing derivatives using the Chebyshev differentiation matrix
    • Bayliss A., Class A., and Matkowsky B.J. Roundoff error in computing derivatives using the Chebyshev differentiation matrix. J. Comput. Phys. 116 (1995) 380-383
    • (1995) J. Comput. Phys. , vol.116 , pp. 380-383
    • Bayliss, A.1    Class, A.2    Matkowsky, B.J.3
  • 3
    • 84966227395 scopus 로고
    • Some spectral approximations of two-dimensional fourth-order problems
    • Bernardi C., Coppoletta G., and Maday Y. Some spectral approximations of two-dimensional fourth-order problems. Math. Comput. 59 (1992) 63-76
    • (1992) Math. Comput. , vol.59 , pp. 63-76
    • Bernardi, C.1    Coppoletta, G.2    Maday, Y.3
  • 4
    • 67349095304 scopus 로고    scopus 로고
    • Spectral methods
    • Ciarlet P.G., and Lions J.L. (Eds), Elsevier Science, North-Holland
    • Bernardi C., and Maday Y. Spectral methods. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis vol. 5 (1997), Elsevier Science, North-Holland 209-485
    • (1997) Handbook of Numerical Analysis , vol.5 , pp. 209-485
    • Bernardi, C.1    Maday, Y.2
  • 7
    • 84966247397 scopus 로고
    • Generation of finite difference formulas on arbitrarily spaced grids
    • Fornberg B. Generation of finite difference formulas on arbitrarily spaced grids. Math. Comput. 51 (1988) 699-706
    • (1988) Math. Comput. , vol.51 , pp. 699-706
    • Fornberg, B.1
  • 10
    • 0008485957 scopus 로고
    • A spectral multigrid method for the Stokes problem in streamfunction formulation
    • Heinrichs W. A spectral multigrid method for the Stokes problem in streamfunction formulation. J. Comput. Phys. 102 (1992) 310-318
    • (1992) J. Comput. Phys. , vol.102 , pp. 310-318
    • Heinrichs, W.1
  • 11
    • 33645011039 scopus 로고    scopus 로고
    • Radial basis function Hermite collocation approach for the numerical simulation of the effect of precipitation inhibitor on the crystallization process of an over-saturated solution
    • Hernandez Rosales A., La Rocca A., and Power H. Radial basis function Hermite collocation approach for the numerical simulation of the effect of precipitation inhibitor on the crystallization process of an over-saturated solution. Numer. Methods Partial Differential Equations 22 (2006) 361-380
    • (2006) Numer. Methods Partial Differential Equations , vol.22 , pp. 361-380
    • Hernandez Rosales, A.1    La Rocca, A.2    Power, H.3
  • 12
    • 0000689353 scopus 로고
    • The pseudospectral method for solving differential eigenvalue problems
    • Huang W., and Sloan D.M. The pseudospectral method for solving differential eigenvalue problems. J. Comput. Phys. 111 (1994) 399-409
    • (1994) J. Comput. Phys. , vol.111 , pp. 399-409
    • Huang, W.1    Sloan, D.M.2
  • 13
    • 3142729350 scopus 로고    scopus 로고
    • A volumetric integral radial basis function method for time-dependent partial differential equations: I. Formulation
    • Kansa E.J., Power H., Fasshauer G.E., and Ling L. A volumetric integral radial basis function method for time-dependent partial differential equations: I. Formulation. Eng. Anal. Boundary Elements 28 (2004) 1191-1206
    • (2004) Eng. Anal. Boundary Elements , vol.28 , pp. 1191-1206
    • Kansa, E.J.1    Power, H.2    Fasshauer, G.E.3    Ling, L.4
  • 14
    • 0038220863 scopus 로고
    • A note on the satisfaction of the boundary conditions for Chebyshev collocation methods in rectangular domains
    • Karageorghis A. A note on the satisfaction of the boundary conditions for Chebyshev collocation methods in rectangular domains. J. Scientific Comput. 6 (1991) 21-26
    • (1991) J. Scientific Comput. , vol.6 , pp. 21-26
    • Karageorghis, A.1
  • 15
    • 38149146040 scopus 로고
    • Satisfaction of boundary conditions for Chebyshev collocation methods in cuboidal domains
    • Karageorghis A. Satisfaction of boundary conditions for Chebyshev collocation methods in cuboidal domains. Comput. Math. Appl. 27 (1994) 85-90
    • (1994) Comput. Math. Appl. , vol.27 , pp. 85-90
    • Karageorghis, A.1
  • 16
    • 14644407531 scopus 로고    scopus 로고
    • Multiquadric collocation method with integral formulation for boundary layer problems
    • Ling L., and Trummer M.R. Multiquadric collocation method with integral formulation for boundary layer problems. Comput. Math. Appl. 48 5-6 (2004) 927-941
    • (2004) Comput. Math. Appl. , vol.48 , Issue.5-6 , pp. 927-941
    • Ling, L.1    Trummer, M.R.2
  • 17
    • 84966244353 scopus 로고
    • Multivariate interpolation and conditionally positive definite functions, II
    • Madych W.R., and Nelson S.A. Multivariate interpolation and conditionally positive definite functions, II. Math. Comput. 54 189 (1990) 211-230
    • (1990) Math. Comput. , vol.54 , Issue.189 , pp. 211-230
    • Madych, W.R.1    Nelson, S.A.2
  • 18
    • 13244255578 scopus 로고    scopus 로고
    • Solving high order ordinary differential equations with radial basis function networks
    • Mai-Duy N. Solving high order ordinary differential equations with radial basis function networks. Int. J. Numer. Methods Eng. 62 (2005) 824-852
    • (2005) Int. J. Numer. Methods Eng. , vol.62 , pp. 824-852
    • Mai-Duy, N.1
  • 19
    • 33846174963 scopus 로고    scopus 로고
    • N. Mai-Duy, An effective spectral collocation method for the direct solution of high-order ODEs, Comm. Numer. Methods Eng., in press.
  • 20
    • 22244445527 scopus 로고    scopus 로고
    • Solving high order partial differential equations with radial basis function networks
    • Mai-Duy N., and Tanner R.I. Solving high order partial differential equations with radial basis function networks. Int. J. Numer. Methods Eng. 63 (2005) 1636-1654
    • (2005) Int. J. Numer. Methods Eng. , vol.63 , pp. 1636-1654
    • Mai-Duy, N.1    Tanner, R.I.2
  • 22
    • 33846181889 scopus 로고    scopus 로고
    • J.C. Mason, T.N. Phillips (Guest Editors), Numerical Algorithms, vol. 38, Number 1, Chebyshev Polynomials and Spectral Methods, 2005.
  • 24
    • 0025448724 scopus 로고
    • On the coefficients of integrated expansions of ultraspherical polynomials
    • Phillips T.N., and Karageorghis A. On the coefficients of integrated expansions of ultraspherical polynomials. SIAM J. Numer. Anal. 27 3 (1990) 823-830
    • (1990) SIAM J. Numer. Anal. , vol.27 , Issue.3 , pp. 823-830
    • Phillips, T.N.1    Karageorghis, A.2
  • 28
    • 0001216115 scopus 로고    scopus 로고
    • Generation of pseudospectral differentiation matrices I
    • Welfert B.D. Generation of pseudospectral differentiation matrices I. SIAM J. Numer. Anal. 34 (1997) 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.