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Volumn 171, Issue 1, 2005, Pages 646-674

Numerical integration over smooth surfaces in ℝ3 via class φm variable transformations. Part I: Smooth integrands

Author keywords

Asymptotic expansions; Euler Maclaurin expansions; Integration over smooth surfaces in 3; Numerical integration; Product trapezoidal rule; Sin m transformation; Variable transformations

Indexed keywords

COMPUTATION THEORY; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; INTEGRAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; NUMERICAL ANALYSIS; VARIABLE FREQUENCY OSCILLATORS;

EID: 28444460202     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2005.01.077     Document Type: Article
Times cited : (6)

References (25)
  • 2
    • 0004998311 scopus 로고    scopus 로고
    • The numerical solution of boundary integral equations
    • I.S. Duff G.A. Watson Oxford University Press Oxford
    • K.E. Atkinson The numerical solution of boundary integral equations I.S. Duff G.A. Watson State of the Art in Numerical Analysis 1997 Oxford University Press Oxford 223 259
    • (1997) State of the Art in Numerical Analysis , pp. 223-259
    • Atkinson, K.E.1
  • 3
    • 0012707577 scopus 로고    scopus 로고
    • The numerical solution of integral equations of the second kind
    • Cambridge University Press Cambridge
    • K.E. Atkinson The numerical solution of integral equations of the second kind Cambridge Monographs on Applied and Computational Mathematics no. 4 1997 Cambridge University Press Cambridge
    • (1997) Cambridge Monographs on Applied and Computational Mathematics , vol.4
    • Atkinson, K.E.1
  • 4
    • 23844463165 scopus 로고    scopus 로고
    • Quadrature of singular integrands over surfaces
    • K.E. Atkinson Quadrature of singular integrands over surfaces Electr. Trans. Numer. Anal. 17 2004 133 150
    • (2004) Electr. Trans. Numer. Anal. , vol.17 , pp. 133-150
    • Atkinson, K.E.1
  • 6
    • 0002374955 scopus 로고    scopus 로고
    • Sigmoidal transformations and the trapezoidal rule
    • D. Elliott Sigmoidal transformations and the trapezoidal rule J. Austral. Math. Soc., Ser. B (E) 40 1998 E77 E137
    • (1998) J. Austral. Math. Soc., Ser. B (E) , vol.40
    • Elliott, D.1
  • 7
    • 0033318245 scopus 로고    scopus 로고
    • D2lri: A nonadaptive algorithm for two-dimensional cubature
    • M. Hill, and I. Robinson d2lri: A nonadaptive algorithm for two-dimensional cubature J. Comp. Appl. Math. 112 1999 121 145
    • (1999) J. Comp. Appl. Math. , vol.112 , pp. 121-145
    • Hill, M.1    Robinson, I.2
  • 10
    • 0029720546 scopus 로고    scopus 로고
    • Periodizing transformations for numerical integration
    • D.P. Laurie Periodizing transformations for numerical integration J. Comp. Appl. Math. 66 1996 337 344
    • (1996) J. Comp. Appl. Math. , vol.66 , pp. 337-344
    • Laurie, D.P.1
  • 11
    • 84948301871 scopus 로고
    • Development of non-linear transformations for improving convergence of sequences
    • D. Levin Development of non-linear transformations for improving convergence of sequences Int. J. Comp. Math. B 3 1973 371 388
    • (1973) Int. J. Comp. Math. B , vol.3 , pp. 371-388
    • Levin, D.1
  • 12
    • 84998260480 scopus 로고
    • An IMT-type double exponential formula for numerical integration
    • M. Mori An IMT-type double exponential formula for numerical integration Publ. Res. Inst. Math. Sci. Kyoto Univ. 14 1978 713 729
    • (1978) Publ. Res. Inst. Math. Sci. Kyoto Univ. , vol.14 , pp. 713-729
    • Mori, M.1
  • 14
    • 0039483058 scopus 로고    scopus 로고
    • Algorithm 816: R2d2lri: An algorithm for automatic two-dimensional cubature
    • I. Robinson, and M. Hill Algorithm 816: r2d2lri: An algorithm for automatic two-dimensional cubature ACM Trans. Math. Software 28 2002 75 100
    • (2002) ACM Trans. Math. Software , vol.28 , pp. 75-100
    • Robinson, I.1    Hill, M.2
  • 15
    • 84968521902 scopus 로고
    • Numerical evaluation of high-dimensional integrals
    • T.W. Sag, and G. Szekeres Numerical evaluation of high-dimensional integrals Math. Comp. 18 1964 245 253
    • (1964) Math. Comp. , vol.18 , pp. 245-253
    • Sag, T.W.1    Szekeres, G.2
  • 16
    • 85171863190 scopus 로고
    • Nonlinear transformations of divergent and slowly convergent sequences
    • D. Shanks Nonlinear transformations of divergent and slowly convergent sequences J. Math. Phys. 34 1955 1 42
    • (1955) J. Math. Phys. , vol.34 , pp. 1-42
    • Shanks, D.1
  • 17
    • 0000046873 scopus 로고
    • A new variable transformation for numerical integration
    • H. Brass G. Hämmerlin ISNM 112 Birkhäuser Basel
    • A. Sidi A new variable transformation for numerical integration H. Brass G. Hämmerlin Numerical Integration IV ISNM 112 1993 Birkhäuser Basel 359 373
    • (1993) Numerical Integration IV , pp. 359-373
    • Sidi, A.1
  • 18
    • 23844493437 scopus 로고    scopus 로고
    • Preprint, Computer Science Dept., Technion-Israel Institute of Technology
    • 3, Preprint, Computer Science Dept., Technion-Israel Institute of Technology, 2003.
    • (2003) 3
    • Sidi, A.1
  • 20
    • 23844454585 scopus 로고    scopus 로고
    • Practical extrapolation methods: Theory and applications
    • Cambridge University Press Cambridge
    • A. Sidi Practical extrapolation methods: theory and applications Cambridge Monographs on Applied and Computational Mathematics no. 10 2003 Cambridge University Press Cambridge
    • (2003) Cambridge Monographs on Applied and Computational Mathematics , vol.10
    • Sidi, A.1
  • 21
    • 4544369789 scopus 로고    scopus 로고
    • Euler-Maclaurin expansions for integrals with endpoint singularities: A new perspective
    • A. Sidi Euler-Maclaurin expansions for integrals with endpoint singularities: a new perspective Numer. Math. 98 2004 371 387
    • (2004) Numer. Math. , vol.98 , pp. 371-387
    • Sidi, A.1
  • 22
    • 28444482869 scopus 로고    scopus 로고
    • Extension of a class of periodizing variable transformations for numerical integration
    • in press
    • A. Sidi, Extension of a class of periodizing variable transformations for numerical integration, Math. Comp., in press.
    • Math. Comp.
    • Sidi, A.1
  • 24
    • 0043234051 scopus 로고    scopus 로고
    • Error expansions for multidimensional trapezoidal rules with Sidi transformations
    • P. Verlinden, D.M. Potts, and J.N. Lyness Error expansions for multidimensional trapezoidal rules with Sidi transformations Numer. Algorithms 16 1997 321 347
    • (1997) Numer. Algorithms , vol.16 , pp. 321-347
    • Verlinden, P.1    Potts, D.M.2    Lyness, J.N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.