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Volumn 207, Issue 2, 2007, Pages 301-322

Analytical methods for an elliptic singular perturbation problem in a circle

Author keywords

Boundary value problem; Elliptic equations; Series solution; Singular perturbations; Uniform asymptotic expansion

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC ANALYSIS; BESSEL FUNCTIONS; BOUNDARY LAYERS; FOURIER SERIES; PERTURBATION TECHNIQUES;

EID: 34547127425     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.10.049     Document Type: Article
Times cited : (11)

References (29)
  • 1
    • 34547122021 scopus 로고    scopus 로고
    • M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC, 1964.
  • 2
    • 33846178567 scopus 로고
    • The zeros of Hankel functions as functions of their order
    • Alan Cochran J. The zeros of Hankel functions as functions of their order. Numer. Math. 7 (1965) 238-250
    • (1965) Numer. Math. , vol.7 , pp. 238-250
    • Alan Cochran, J.1
  • 3
    • 0242543400 scopus 로고
    • Sur les zéros des fonctions de Bessel considérées comme fonction de l'ordre
    • Coulomb M.J. Sur les zéros des fonctions de Bessel considérées comme fonction de l'ordre. Bull. Sci. Math. 60 (1936) 297-302
    • (1936) Bull. Sci. Math. , vol.60 , pp. 297-302
    • Coulomb, M.J.1
  • 4
    • 84972494088 scopus 로고
    • The roots of trigonometric integrals
    • de Bruijn N.G. The roots of trigonometric integrals. Duke Math. J. 17 (1950) 197-225
    • (1950) Duke Math. J. , vol.17 , pp. 197-225
    • de Bruijn, N.G.1
  • 5
    • 0001416385 scopus 로고
    • Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter
    • Dunster T.M. Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter. SIAM J. Math. Anal. 21 4 (1990) 995-1018
    • (1990) SIAM J. Math. Anal. , vol.21 , Issue.4 , pp. 995-1018
    • Dunster, T.M.1
  • 6
    • 0010540006 scopus 로고
    • Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type
    • Eckhaus W., and de Jager E.M. Asymptotic solutions of singular perturbation problems for linear differential equations of elliptic type. Arch. Rational Mech. Anal. 23 (1966) 26-86
    • (1966) Arch. Rational Mech. Anal. , vol.23 , pp. 26-86
    • Eckhaus, W.1    de Jager, E.M.2
  • 7
    • 34547094151 scopus 로고    scopus 로고
    • A. Erdélyi, W. Magnus, F. Oberhettinger, F.G. Tricomi, Tables of Integral Transforms, 2 volumes, McGraw-Hill Book Company, Inc., New York, Toronto, London, 1954 (based, in part, on notes left by Harry Bateman).
  • 8
    • 84950658093 scopus 로고
    • Magnetohydrodynamic pipe flow. I
    • Gold R.R. Magnetohydrodynamic pipe flow. I. J. Fluid Mech. 13 (1962) 505-512
    • (1962) J. Fluid Mech. , vol.13 , pp. 505-512
    • Gold, R.R.1
  • 10
    • 0030419987 scopus 로고    scopus 로고
    • A singularly perturbed model problem for numerical computation
    • Hemker P.W. A singularly perturbed model problem for numerical computation. J. Comput. Appl. Math. 76 1-2 (1996) 277-285
    • (1996) J. Comput. Appl. Math. , vol.76 , Issue.1-2 , pp. 277-285
    • Hemker, P.W.1
  • 11
    • 0010575871 scopus 로고
    • y + C (x, y) u = D (x, y) for small ε{lunate}
    • y + C (x, y) u = D (x, y) for small ε{lunate}. Ann. Math. 51 2 (1950) 428-445
    • (1950) Ann. Math. , vol.51 , Issue.2 , pp. 428-445
    • Levinson, N.1
  • 12
    • 3543062315 scopus 로고    scopus 로고
    • Analytic approximations for a singularly perturbed convection-diffusion problem with discontinuous data in a half-infinite strip
    • López J.L., and Sinusía E.P. Analytic approximations for a singularly perturbed convection-diffusion problem with discontinuous data in a half-infinite strip. Acta Appl. Math. 82 1 (2004) 101-117
    • (2004) Acta Appl. Math. , vol.82 , Issue.1 , pp. 101-117
    • López, J.L.1    Sinusía, E.P.2
  • 13
    • 3042794565 scopus 로고    scopus 로고
    • Asymptotic expansions for two singularly perturbed convection-diffusion problems with discontinuous data: the quarter plane and the infinite strip
    • López J.L., and Sinusía E.P. Asymptotic expansions for two singularly perturbed convection-diffusion problems with discontinuous data: the quarter plane and the infinite strip. Stud. Appl. Math. 113 1 (2004) 57-89
    • (2004) Stud. Appl. Math. , vol.113 , Issue.1 , pp. 57-89
    • López, J.L.1    Sinusía, E.P.2
  • 14
    • 27744534006 scopus 로고    scopus 로고
    • Asymptotic approximation of singularly perturbed convection-diffusion problems with discontinuous derivatives of the Dirichlet data
    • López J.L., and Sinusía E.P. Asymptotic approximation of singularly perturbed convection-diffusion problems with discontinuous derivatives of the Dirichlet data. Quart. Appl. Math. 63 3 (2005) 527-543
    • (2005) Quart. Appl. Math. , vol.63 , Issue.3 , pp. 527-543
    • López, J.L.1    Sinusía, E.P.2
  • 15
    • 19444365238 scopus 로고    scopus 로고
    • Asymptotic approximations for a singularly perturbed convection-diffusion problem with discontinuous data in a sector
    • López J.L., and Sinusía E.P. Asymptotic approximations for a singularly perturbed convection-diffusion problem with discontinuous data in a sector. J. Comput. Appl. Math. 181 1 (2005) 1-23
    • (2005) J. Comput. Appl. Math. , vol.181 , Issue.1 , pp. 1-23
    • López, J.L.1    Sinusía, E.P.2
  • 16
    • 34547101507 scopus 로고    scopus 로고
    • J.L. López, E.P. Sinusía, N.M. Temme, Asymptotic behaviour of three-dimensional singularly perturbed convection-diffusion problems with discontinuous data, J. Math. Anal. Appl., 2006, accepted for publication.
  • 17
    • 85153245564 scopus 로고    scopus 로고
    • J.L. López, E.P. Sinusía, N.M. Temme, First order approximation of an elliptic 3D singular perturbation problem, Stud. Appl. Math. 116 (2006) 303-319.
  • 20
    • 84950623950 scopus 로고
    • Magnetohydrodynamic pipe flow. II. High Hartmann number
    • Shercliff J.A. Magnetohydrodynamic pipe flow. II. High Hartmann number. J. Fluid Mech. 13 (1962) 513-518
    • (1962) J. Fluid Mech. , vol.13 , pp. 513-518
    • Shercliff, J.A.1
  • 21
    • 0010574728 scopus 로고    scopus 로고
    • A novel uniform expansion for a singularly perturbed parabolic problem with corner singularity
    • Shih S.-D. A novel uniform expansion for a singularly perturbed parabolic problem with corner singularity. Methods Appl. Anal. 3 2 (1996) 203-227
    • (1996) Methods Appl. Anal. , vol.3 , Issue.2 , pp. 203-227
    • Shih, S.-D.1
  • 22
    • 3042759608 scopus 로고    scopus 로고
    • Angular layer of a singularly perturbed parabolic problem with corner singularity
    • Shih S.-D. Angular layer of a singularly perturbed parabolic problem with corner singularity. Canad. Appl. Math. Quart. 9 2 (2001) 159-188
    • (2001) Canad. Appl. Math. Quart. , vol.9 , Issue.2 , pp. 159-188
    • Shih, S.-D.1
  • 23
    • 3042840889 scopus 로고
    • Analytical methods for a singular perturbation problem in a sector
    • Temme N.M. Analytical methods for a singular perturbation problem in a sector. SIAM J. Math. Anal. 5 (1974) 876-887
    • (1974) SIAM J. Math. Anal. , vol.5 , pp. 876-887
    • Temme, N.M.1
  • 25
    • 84971194621 scopus 로고
    • Steady longitudinal motion of an insulating cylinder in a conducting fluid
    • Waechter R.T. Steady longitudinal motion of an insulating cylinder in a conducting fluid. Proc. Cambridge Philos. Soc. 64 (1968) 1165-1201
    • (1968) Proc. Cambridge Philos. Soc. , vol.64 , pp. 1165-1201
    • Waechter, R.T.1
  • 26
    • 84972492726 scopus 로고
    • Asymptotic solution of boundary value problems for the differential equation Δ U + λ ∂ U / ∂ x = λ f (x, y)
    • Wasow W. Asymptotic solution of boundary value problems for the differential equation Δ U + λ ∂ U / ∂ x = λ f (x, y). Duke Math. J. 11 (1944) 405-415
    • (1944) Duke Math. J. , vol.11 , pp. 405-415
    • Wasow, W.1
  • 29
    • 84953751498 scopus 로고
    • Trigonometric Series
    • Cambridge University Press, New York Reprinted by Cambridge University Press, 1988
    • Zygmund A. Trigonometric Series. second ed. vols. I, II (1959), Cambridge University Press, New York Reprinted by Cambridge University Press, 1988
    • (1959) second ed. , vol.1-2
    • Zygmund, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.