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Volumn 103, Issue 4, 2006, Pages 575-590

An algebraic approach to invariant preserving integators: The case of quadratic and hamiltonian invariants

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EID: 33744721734     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-006-0003-8     Document Type: Article
Times cited : (92)

References (19)
  • 1
    • 8144231442 scopus 로고    scopus 로고
    • Trees, renormalization and differential equations
    • Brouder, Ch.: Trees, renormalization and differential equations. BIT 44(3), 425-438 (2004)
    • (2004) BIT , vol.44 , Issue.3 , pp. 425-438
    • Brouder, Ch.1
  • 2
    • 0001018465 scopus 로고
    • On quadratic invariants and symplectic structure
    • Bochev, P.B., Scovel, C.: On quadratic invariants and symplectic structure. BIT 34, 337-345 (1994)
    • (1994) BIT , vol.34 , pp. 337-345
    • Bochev, P.B.1    Scovel, C.2
  • 3
    • 0003019535 scopus 로고
    • The effective order of Runge-Kutta methods
    • Morris, J.Ll. (ed) Proceedings of conference on the numerical solution of differential equations
    • Butcher, J.C.: The effective order of Runge-Kutta methods. In: Morris, J.Ll. (ed) Proceedings of conference on the numerical solution of differential equations, vol 109 of Lecture Notes in Math., pp 133-139 (1969)
    • (1969) Lecture Notes in Math. , vol.109 , pp. 133-139
    • Butcher, J.C.1
  • 4
    • 84968481790 scopus 로고
    • An algebraic theory of integration methods
    • Butcher, J.C.: An algebraic theory of integration methods. Math. Comput. 26, 79-106 (1972)
    • (1972) Math. Comput. , vol.26 , pp. 79-106
    • Butcher, J.C.1
  • 7
    • 33744742455 scopus 로고    scopus 로고
    • A substitution law for B-series vector fields
    • INRIA, France
    • Chartier, P., Hairer, E., Vilmart, G.: A substitution law for B-series vector fields. Technical Report 5498, INRIA, France (2005)
    • (2005) Technical Report , vol.5498
    • Chartier, P.1    Hairer, E.2    Vilmart, G.3
  • 8
    • 0032257297 scopus 로고    scopus 로고
    • Hopf algebras, renormalization and noncommutative geometry
    • Connes, A., Kreimer, D.: Hopf algebras, renormalization and noncommutative geometry. Commun. Math. Phys. 199, 203-242 (1998)
    • (1998) Commun. Math. Phys. , vol.199 , pp. 203-242
    • Connes, A.1    Kreimer, D.2
  • 9
    • 18244388472 scopus 로고    scopus 로고
    • Energy conservation with non-symplectic methods: Examples and counter-examples
    • Faou, E., Hairer, E., Pham, T.L.: Energy conservation with non-symplectic methods: examples and counter-examples. BIT 44, 699-709 (2004)
    • (2004) BIT , vol.44 , pp. 699-709
    • Faou, E.1    Hairer, E.2    Pham, T.L.3
  • 10
    • 0000566698 scopus 로고
    • Backward analysis of numerical integrators and symplectic methods
    • Hairer, E.: Backward analysis of numerical integrators and symplectic methods. Ann. Numer. Math. 1, 107-132 (1994)
    • (1994) Ann. Numer. Math. , vol.1 , pp. 107-132
    • Hairer, E.1
  • 11
    • 22844456938 scopus 로고    scopus 로고
    • Backward error analysis for multistep methods
    • Hairer, E.: Backward error analysis for multistep methods. Numer. Math. 84, 199-232 (1999)
    • (1999) Numer. Math. , vol.84 , pp. 199-232
    • Hairer, E.1
  • 12
    • 3142580393 scopus 로고    scopus 로고
    • Symmetric multistep methods over long times
    • Hairer, E., Lubich, C.: Symmetric multistep methods over long times. Numer. Math. 97, 699-723 (2004)
    • (2004) Numer. Math. , vol.97 , pp. 699-723
    • Hairer, E.1    Lubich, C.2
  • 13
    • 0015960381 scopus 로고
    • On the Butcher group and general multi-value methods
    • Hairer, E., Wanner, G.: On the Butcher group and general multi-value methods. Computing 13, 1-15 (1974)
    • (1974) Computing , vol.13 , pp. 1-15
    • Hairer, E.1    Wanner, G.2
  • 14
    • 0012912813 scopus 로고
    • Solving Ordinary differential equations I. Nonstiff problems
    • 2nd edn. Berlin Heidelberg New york: Springer
    • Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary differential equations I. Nonstiff problems. Springer Series in Computational Mathematics, vol 8, 2nd edn. Berlin Heidelberg New york: Springer 1993
    • (1993) Springer Series in Computational Mathematics , vol.8
    • Hairer, E.1    Nørsett, S.P.2    Wanner, G.3
  • 15
    • 0013460577 scopus 로고    scopus 로고
    • Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations
    • Berlin Heidelberg New york: Springer
    • Hairer, E., Lubich, C., Wanner, G.: Geometric numerical integration. Structure-preserving algorithms for ordinary differential equations. Springer Series in Computational Mathematics, vol 31. Berlin Heidelberg New york: Springer 2002
    • (2002) Springer Series in Computational Mathematics , vol.31
    • Hairer, E.1    Lubich, C.2    Wanner, G.3
  • 16
    • 0011895293 scopus 로고
    • Multi-step methods are essentially one-step methods
    • Kirchgraber, U.: Multi-step methods are essentially one-step methods. Numer. Math. 48, 85-90 (1986)
    • (1986) Numer. Math. , vol.48 , pp. 85-90
    • Kirchgraber, U.1
  • 18
    • 0033077759 scopus 로고    scopus 로고
    • Formal series and numerical integrators, part i: Systems of ODEs and symplectic integrators
    • Murua, A.: Formal series and numerical integrators, part i: systems of ODEs and symplectic integrators. Appl. Numer. Math. 29, 221-251 (1999)
    • (1999) Appl. Numer. Math. , vol.29 , pp. 221-251
    • Murua, A.1
  • 19
    • 33744773993 scopus 로고    scopus 로고
    • The Hopf algebra of rooted trees, free Lie algebras, and Lie series
    • Accepted for publication
    • Murua, A.: The Hopf algebra of rooted trees, free Lie algebras, and Lie series. Accepted for publication in FOCM, 2005
    • (2005) FOCM
    • Murua, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.