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Volumn 40, Issue 1, 2005, Pages 79-100

New a posteriori error estimates for singular boundary value problems

Author keywords

A posteriori error estimation; Boundary value problems; Collocation; Defect correction; Essential singularity; Ordinary differential equations

Indexed keywords


EID: 22944487943     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11075-005-3791-5     Document Type: Article
Times cited : (12)

References (27)
  • 2
    • 17644362234 scopus 로고    scopus 로고
    • Globale Fehlerschätzer für Randwertprobleme mit einer Singularität zweiter Art
    • Institute for Appl. Math. and Numer. Anal., Vienna University of Technology, Austria
    • W. Auzinger, E. Karner, O. Koch, D. Praetorius and E. Weinmüller, Globale Fehlerschätzer für Randwertprobleme mit einer Singularität zweiter Art, Technical Report ANUM Preprint Nr. 6/03, Institute for Appl. Math. and Numer. Anal., Vienna University of Technology, Austria; available at http://www.math.tuwien.ac.at/~inst115/preprints.htm (2003).
    • (2003) Technical Report ANUM Preprint Nr. 6/03 , vol.6 , Issue.3
    • Auzinger, W.1    Karner, E.2    Koch, O.3    Praetorius, D.4    Weinmüller, E.5
  • 3
    • 0041375531 scopus 로고    scopus 로고
    • A collocation code for boundary value problems in ordinary differential equations
    • W. Auzinger, G. Kneisl, O. Koch and E. Weinmüller, A collocation code for boundary value problems in ordinary differential equations, Numer. Algorithms 33 (2003) 27-39.
    • (2003) Numer. Algorithms , vol.33 , pp. 27-39
    • Auzinger, W.1    Kneisl, G.2    Koch, O.3    Weinmüller, E.4
  • 4
    • 22944445227 scopus 로고    scopus 로고
    • Numerical solution of boundary value problems with an essential singularity
    • Institute for Appl. Math, and Numer. Anal., Vienna University of Technology, Austria
    • W. Auzinger, O. Koch, J. Petrickovic and E. Weinmüller, Numerical solution of boundary value problems with an essential singularity, Technical Report ANUM Preprint Nr. 3/03, Institute for Appl. Math, and Numer. Anal., Vienna University of Technology, Austria; available at http: //www.math.tuwien.ac.at/~inst115/preprints.htm(2003).
    • (2003) Technical Report ANUM Preprint Nr. 3/03 , vol.3 , Issue.3
    • Auzinger, W.1    Koch, O.2    Petrickovic, J.3    Weinmüller, E.4
  • 5
    • 29144523012 scopus 로고    scopus 로고
    • Analysis of a new error estimate for collocation methods applied to singular boundary value problems
    • to appear in
    • W. Auzinger, O. Koch and E. Weinmüller, Analysis of a new error estimate for collocation methods applied to singular boundary value problems, to appear in SIAM J. Numer. Anal; also available at http://www.math.tuwien.ac.at/ ~inst115/preprints.htm/.
    • SIAM J. Numer. Anal
    • Auzinger, W.1    Koch, O.2    Weinmüller, E.3
  • 6
    • 17644397845 scopus 로고    scopus 로고
    • Efficient mesh selection for collocation methods applied to singular B VPs
    • W. Auzinger, O. Koch and E. Weinmüller, Efficient mesh selection for collocation methods applied to singular B VPs, J. Comput. Appl. Math. 180 (2005) 213-227.
    • (2005) J. Comput. Appl. Math. , vol.180 , pp. 213-227
    • Auzinger, W.1    Koch, O.2    Weinmüller, E.3
  • 7
    • 0036437244 scopus 로고    scopus 로고
    • Efficient collocation schemes for singular boundary value problems
    • W. Auzinger, O. Koch and E. Weinmüller, Efficient collocation schemes for singular boundary value problems, Numer. Algorithms 31 (2002) 5-25.
    • (2002) Numer. Algorithms , vol.31 , pp. 5-25
    • Auzinger, W.1    Koch, O.2    Weinmüller, E.3
  • 8
    • 3142704422 scopus 로고    scopus 로고
    • New variants of defect correction for boundary value problems in ordinary differential equations
    • Current Trends in Scientific Computing, eds. Z. Chen, R. Glowinski and K. Li, Amer. Math. Soc., Providence, RI
    • W. Auzinger, O. Koch and E. Weinmüller, New variants of defect correction for boundary value problems in ordinary differential equations, in: Current Trends in Scientific Computing, eds. Z. Chen, R. Glowinski and K. Li, AMS Series in Contemporary Mathematics, Vol. 329 (Amer. Math. Soc., Providence, RI, 2003) pp. 43-50.
    • (2003) AMS Series in Contemporary Mathematics , vol.329 , pp. 43-50
    • Auzinger, W.1    Koch, O.2    Weinmüller, E.3
  • 9
    • 22944443631 scopus 로고    scopus 로고
    • Collocation methods for boundary value problems with an essential singularity
    • Large-Scale Scientific Computing, eds. I. Lirkov, S. Margenov, J. Wasniewski and P. Yalamov, Springer, New York
    • W. Auzinger, O. Koch and E. Weinmüller, Collocation methods for boundary value problems with an essential singularity, in: Large-Scale Scientific Computing, eds. I. Lirkov, S. Margenov, J. Wasniewski and P. Yalamov, Lecture Notes in Computer Science, Vol. 2907 (Springer, New York, 2004) pp. 347-354.
    • (2004) Lecture Notes in Computer Science , vol.2907 , pp. 347-354
    • Auzinger, W.1    Koch, O.2    Weinmüller, E.3
  • 11
    • 0000319158 scopus 로고
    • Collocation at Gaussian points
    • C. d. Boor and B. Swartz, Collocation at Gaussian points, SIAM J. Numer. Anal. 10 (1973) 582-606.
    • (1973) SIAM J. Numer. Anal. , vol.10 , pp. 582-606
    • Boor, C.D.1    Swartz, B.2
  • 12
    • 0035824457 scopus 로고    scopus 로고
    • Symmetry-adapted moving mesh schemes for the nonlinear Schrödinger equation
    • C. Budd and V. Dorodnitsyn, Symmetry-adapted moving mesh schemes for the nonlinear Schrödinger equation, J. Phys. A Meth. Gen. 34 (2001) 10387-10400.
    • (2001) J. Phys. A Meth. Gen. , vol.34 , pp. 10387-10400
    • Budd, C.1    Dorodnitsyn, V.2
  • 13
    • 0012530571 scopus 로고
    • On the imperfection sensitivity of complete spherical shells
    • M. Drmota, R. Scheidl, H. Troger and E. Weinmüller, On the imperfection sensitivity of complete spherical shells, Comp. Mech. 2 (1987) 63-74.
    • (1987) Comp. Mech. , vol.2 , pp. 63-74
    • Drmota, M.1    Scheidl, R.2    Troger, H.3    Weinmüller, E.4
  • 14
    • 0041774330 scopus 로고
    • Iterated defect correction for differential equations, part I: Theoretical results
    • R. Frank and C. Überhuber, Iterated defect correction for differential equations, part I: Theoretical results, Computing 20 (1978) 207-228.
    • (1978) Computing , vol.20 , pp. 207-228
    • Frank, R.1    Überhuber, C.2
  • 15
    • 0017011164 scopus 로고
    • Difference methods for boundary value problems with a singularity of the first kind
    • F. d. Hoog and R. Weiss, Difference methods for boundary value problems with a singularity of the first kind, SIAM J. Numer. Anal. 13 (1976) 775-813.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 775-813
    • Hoog, F.D.1    Weiss, R.2
  • 16
    • 0002102438 scopus 로고
    • Collocation methods for singular boundary value problems
    • F. d. Hoog and R. Weiss, Collocation methods for singular boundary value problems, SIAM J. Numer. Anal. 15 (1978) 198-217.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 198-217
    • Hoog, F.D.1    Weiss, R.2
  • 17
    • 0013288006 scopus 로고
    • The numerical solution of boundary value problems with an essential singularity
    • F. d. Hoog and R. Weiss, The numerical solution of boundary value problems with an essential singularity, SIAM J. Numer. Anal. 16 (1979) 637-669.
    • (1979) SIAM J. Numer. Anal. , vol.16 , pp. 637-669
    • Hoog, F.D.1    Weiss, R.2
  • 18
    • 0041867903 scopus 로고
    • On the boundary value problem for systems of ordinary differential equations with a singularity of the second kind
    • F. d. Hoog and R. Weiss, On the boundary value problem for systems of ordinary differential equations with a singularity of the second kind, SIAM J. Math. Anal. 11 (1980) 41-60.
    • (1980) SIAM J. Math. Anal. , vol.11 , pp. 41-60
    • Hoog, F.D.1    Weiss, R.2
  • 19
    • 0001969945 scopus 로고    scopus 로고
    • Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation
    • T. Kapitula, Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation, Nonlinearity 9 (1996) 669-685.
    • (1996) Nonlinearity , vol.9 , pp. 669-685
    • Kapitula, T.1
  • 20
    • 22344440493 scopus 로고    scopus 로고
    • Asymptotically correct error estimation for collocation methods applied to singular boundary value problems
    • O. Koch, Asymptotically correct error estimation for collocation methods applied to singular boundary value problems, Numer. Math. 101(1) (2005) 143-164.
    • (2005) Numer. Math. , vol.101 , Issue.1 , pp. 143-164
    • Koch, O.1
  • 21
    • 17144434591 scopus 로고    scopus 로고
    • Analytical and numerical treatment of a singular initial value problem in avalanche modeling
    • O. Koch and E. Weinmüller, Analytical and numerical treatment of a singular initial value problem in avalanche modeling, Appl. Math. Comput. 148(2) (2003) 561-570.
    • (2003) Appl. Math. Comput. , vol.148 , Issue.2 , pp. 561-570
    • Koch, O.1    Weinmüller, E.2
  • 22
    • 0001595984 scopus 로고
    • Boundary value problems on semi-infinite intervals and their numerical solution
    • M. Lentini and H. Keller, Boundary value problems on semi-infinite intervals and their numerical solution, SIAM J. Numer. Anal. 17(3) (1980) 577-604.
    • (1980) SIAM J. Numer. Anal. , vol.17 , Issue.3 , pp. 577-604
    • Lentini, M.1    Keller, H.2
  • 23
    • 0020145769 scopus 로고
    • Asymptotic analysis of von Karman flows
    • P. Markowich, Asymptotic analysis of von Karman flows, SIAM J. Appl. Math. 42(3) (1982) 549-557.
    • (1982) SIAM J. Appl. Math. , vol.42 , Issue.3 , pp. 549-557
    • Markowich, P.1
  • 24
    • 84966259415 scopus 로고
    • Collocation methods for boundary value problems on "long" intervals
    • P. Markowich and C. Ringhofer, Collocation methods for boundary value problems on "long" intervals Math. Comp. 40 (1983) 123-150.
    • (1983) Math. Comp. , vol.40 , pp. 123-150
    • Markowich, P.1    Ringhofer, C.2
  • 25
    • 33745580052 scopus 로고
    • The defect correction principle and discretization methods
    • H.J. Stetter, The defect correction principle and discretization methods, Numer. Math. 29 (1978) 425-443.
    • (1978) Numer. Math. , vol.29 , pp. 425-443
    • Stetter, H.J.1
  • 26
    • 0042776264 scopus 로고
    • Collocation for singular boundary value problems of second order
    • E. Weinmuller, Collocation for singular boundary value problems of second order, SIAM J. Numer. Anal. 23 (1986) 1062-1095.
    • (1986) SIAM J. Numer. Anal. , vol.23 , pp. 1062-1095
    • Weinmüller, E.1
  • 27
    • 0007148564 scopus 로고
    • On the estimation of errors propagated in the numerical integration of ODEs
    • P. Zadunaisky, On the estimation of errors propagated in the numerical integration of ODEs, Numer. Math. 27 (1976) 21-39.
    • (1976) Numer. Math. , vol.27 , pp. 21-39
    • Zadunaisky, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.