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Volumn 19, Issue 3, 1999, Pages 375-424

Algorithms for constructing stable manifolds of stationary solutions

Author keywords

[No Author keywords available]

Indexed keywords

AUTONOMOUS SYSTEMS; CONTINUOUS PROBLEMS; DISCRETE DYNAMICAL SYSTEMS; HADAMARD; INDIRECT METHODS; SINGLE POINT; STABLE MANIFOLD; STATIONARY SOLUTIONS;

EID: 0033245794     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/19.3.375     Document Type: Article
Times cited : (10)

References (34)
  • 4
    • 0023427317 scopus 로고
    • On the numerical approximation of phase portraits near stationary points
    • BEYN, W.-J. 1987 On the numerical approximation of phase portraits near stationary points. SIAM J. Numer. Anal. 24, 1095-1113.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1095-1113
    • Beyn, W.-J.1
  • 5
    • 0001340513 scopus 로고
    • The numerical computation of connecting orbits in dynamical systems
    • BEYN, W.-J. 1990 The numerical computation of connecting orbits in dynamical systems. IMA J. Numer. Anal. 9, 379-405.
    • (1990) IMA J. Numer. Anal. , vol.9 , pp. 379-405
    • Beyn, W.-J.1
  • 6
    • 0000339206 scopus 로고
    • Numerical methods for dynamical systems
    • (W. Light, ed). Oxford: Clarendon
    • BEYN, W.-J. 1991 Numerical methods for dynamical systems. Advances in Numerical Analysis (W. Light, ed). Oxford: Clarendon, pp 175-236.
    • (1991) Advances in Numerical Analysis , pp. 175-236
    • Beyn, W.-J.1
  • 9
    • 0017011164 scopus 로고
    • Difference methods for boundary value problems with a singularity of the first kind
    • DE HOOG, F. R. & WEISS, R. 1976 Difference methods for boundary value problems with a singularity of the first kind. SIAM J. Numer. Anal. 13, 775-813.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 775-813
    • De Hoog, F.R.1    Weiss, R.2
  • 10
    • 0002102438 scopus 로고
    • Collocation methods for singular boundary value problems
    • DE HOOG, F. R. & WEISS, R. 1978 Collocation methods for singular boundary value problems. SIAM J. Numer. Anal. 15, 198-217.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 198-217
    • De Hoog, F.R.1    Weiss, R.2
  • 11
    • 0019188385 scopus 로고
    • An approximation theory for boundary value problems on infinite intervals
    • DE HOOG, F. R. & WEISS, R. 1980 An approximation theory for boundary value problems on infinite intervals. Computing 24, 227-239.
    • (1980) Computing , vol.24 , pp. 227-239
    • De Hoog, F.R.1    Weiss, R.2
  • 13
    • 0002747396 scopus 로고
    • AUTO: Software for continuation and bifurcation problems in ODE's
    • Cal. Tech.
    • DOEDEL, E. J. & KERNEVEZ, J. P. 1986 AUTO: Software for continuation and bifurcation problems in ODE's. Appl. Math. Rep., Cal. Tech.
    • (1986) Appl. Math. Rep.
    • Doedel, E.J.1    Kernevez, J.P.2
  • 14
    • 0026170304 scopus 로고
    • Numerical computation and continuation of invariant manifolds connecting fixed points
    • FRIEDMAN, M. J. & DOEDEL, E. J. 1991 Numerical computation and continuation of invariant manifolds connecting fixed points. SIAM J. Numer. Anal. 28, 789-808.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 789-808
    • Friedman, M.J.1    Doedel, E.J.2
  • 18
    • 0000962873 scopus 로고
    • Sur l'iteration et les solutions asymptotiques des equations differentielles
    • HADAMARD, J. 1901 Sur l'iteration et les solutions asymptotiques des equations differentielles. Bull. Soc. Math. France. 29, 224-228.
    • (1901) Bull. Soc. Math. France , vol.29 , pp. 224-228
    • Hadamard, J.1
  • 19
    • 0001389356 scopus 로고
    • On the computation of invariant manifolds of fixed points
    • HOMBURG, A. J., OSINGA, H. M., & VEGTER, G. 1995 On the computation of invariant manifolds of fixed points. Z. Angw. Math. Phys. 46, 171-187.
    • (1995) Z. Angw. Math. Phys. , vol.46 , pp. 171-187
    • Homburg, A.J.1    Osinga, H.M.2    Vegter, G.3
  • 20
    • 0001595984 scopus 로고
    • Boundary value problems over semi-infinite intervals and their numerical solution
    • LENTINI, M. & KELLER, H. B. 1980 Boundary value problems over semi-infinite intervals and their numerical solution. SIAM J. Numer. Anal. 17, 577-604.
    • (1980) SIAM J. Numer. Anal. , vol.17 , pp. 577-604
    • Lentini, M.1    Keller, H.B.2
  • 21
    • 0030621838 scopus 로고    scopus 로고
    • Computation and continuation of homoclinic and heteroclinic orbits with arclength parametrisation
    • LIU, L., MOORE, G., & RUSSELL, R. D. 1997 Computation and continuation of homoclinic and heteroclinic orbits with arclength parametrisation. SIAM J. Sci. Comput. 18, 69-93.
    • (1997) SIAM J. Sci. Comput. , vol.18 , pp. 69-93
    • Liu, L.1    Moore, G.2    Russell, R.D.3
  • 23
    • 21844508391 scopus 로고
    • Computation and parametrisation of periodic and connecting orbits
    • MOORE, G. 1995a Computation and parametrisation of periodic and connecting orbits. IMA J. Numer. Anal. 15, 245-263.
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 245-263
    • Moore, G.1
  • 24
    • 0000264946 scopus 로고
    • Geometric methods for computing invariant manifolds
    • MOORE, G. 1995b Geometric methods for computing invariant manifolds. Appl. Numer. Math. 17, 319-331.
    • (1995) Appl. Numer. Math. , vol.17 , pp. 319-331
    • Moore, G.1
  • 25
    • 0001049214 scopus 로고    scopus 로고
    • Computation and parametrisation of invariant curves and tori
    • MOORE, G. 1996 Computation and parametrisation of invariant curves and tori. SIAM J. Numer. Anal. 33, 2333-2358.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 2333-2358
    • Moore, G.1
  • 28
    • 7944237817 scopus 로고
    • Die stabilitätsfrage bei differentialgleichungssysteme
    • PERRON, O. 1930 Die Stabilitätsfrage bei Differentialgleichungssysteme. Math. Zeit. 32, 703-728.
    • (1930) Math. Zeit. , vol.32 , pp. 703-728
    • Perron, O.1
  • 30
    • 0001234956 scopus 로고
    • A case of the existence of a denumerable set of periodic motions
    • ŠILNIKOV, L. P. 1965 A case of the existence of a denumerable set of periodic motions. Sov. Math. Dokl. 6, 163-166.
    • (1965) Sov. Math. Dokl. , vol.6 , pp. 163-166
    • Šilnikov, L.P.1
  • 33
    • 84974266266 scopus 로고
    • Numerical analysis of dynamical systems
    • (A. Iserles, ed). Cambridge: Cambridge University Press
    • STUART, A.M. 1994 Numerical analysis of dynamical systems. Acta Numerica 1994 (A. Iserles, ed). Cambridge: Cambridge University Press, pp 467-572.
    • (1994) Acta Numerica 1994 , pp. 467-572
    • Stuart, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.