메뉴 건너뛰기




Volumn 12, Issue 4, 2012, Pages 471-508

Erratum to: Higher-Order Averaging, Formal Series and Numerical Integration II: The Quasi-Periodic Case (2012), 12, 471–508, 10.1007/s10208-012-9118-8;Higher-Order Averaging, Formal Series and Numerical Integration II: The Quasi-Periodic Case

Author keywords

Averaging; B series; First integrals; Formal series; Hamiltonian problems; High order averaging; Highly oscillatory problems; Lie algebras; Lie groups; Near integrable systems; Quasi stroboscopic averaging; Trees

Indexed keywords


EID: 84864302262     PISSN: 16153375     EISSN: 16153383     Source Type: Journal    
DOI: 10.1007/s10208-016-9311-2     Document Type: Erratum
Times cited : (31)

References (24)
  • 3
    • 84968481790 scopus 로고
    • An algebraic theory of integration methods
    • J. C. Butcher, An algebraic theory of integration methods, Math. Comput. 26, 79-106 (1972).
    • (1972) Math. Comput. , vol.26 , pp. 79-106
    • Butcher, J.C.1
  • 4
    • 8144231442 scopus 로고    scopus 로고
    • Trees, renormalization and differential equations
    • Ch. Brouder, Trees, renormalization and differential equations, BIT44, 425-438 (2004).
    • (2004) Bit , vol.44 , pp. 425-438
    • Brouder, C.1
  • 6
    • 79960627615 scopus 로고    scopus 로고
    • A stroboscopic method for highly oscillatory problems
    • Lect. Notes Comput. Sci. Eng, B. Engquist, O. Runborg, and R. Tsai (Eds.), Berlin: Springer
    • M. P. Calvo, Ph. Chartier, A. Murua, J. M. Sanz-Serna, A stroboscopic method for highly oscillatory problems, in Numerical Analysis of Multiscale Computations, ed. by B. Engquist, O. Runborg, R. Tsai. Lect. Notes Comput. Sci. Eng., vol. 82 (Springer, Berlin, 2011), pp. 73-87.
    • (2011) Numerical Analysis of Multiscale Computations , vol.82 , pp. 73-87
    • Calvo, M.P.1    Chartier, P.2    Murua, A.3    Sanz-Serna, J.M.4
  • 8
    • 34047115181 scopus 로고    scopus 로고
    • Preserving first integrals and volume forms of additively split systems
    • P. Chartier, A. Murua, Preserving first integrals and volume forms of additively split systems, IMA J. Numer. Anal. 27, 381-405 (2007).
    • (2007) IMA J. Numer. Anal. , vol.27 , pp. 381-405
    • Chartier, P.1    Murua, A.2
  • 9
    • 33744721734 scopus 로고    scopus 로고
    • An algebraic approach to invariant preserving integrators: the case of quadratic and Hamiltonian invariants
    • P. Chartier, E. Faou, A. Murua, An algebraic approach to invariant preserving integrators: the case of quadratic and Hamiltonian invariants, Numer. Math. 103, 575-590 (2006).
    • (2006) Numer. Math. , vol.103 , pp. 575-590
    • Chartier, P.1    Faou, E.2    Murua, A.3
  • 10
    • 77957931902 scopus 로고    scopus 로고
    • Higher-order averaging, formal series and numerical integration I: B-series
    • P. Chartier, A. Murua, J. M. Sanz-Serna, Higher-order averaging, formal series and numerical integration I: B-series, Found. Comput. Math. 10, 695-727 (2010).
    • (2010) Found. Comput. Math. , vol.10 , pp. 695-727
    • Chartier, P.1    Murua, A.2    Sanz-Serna, J.M.3
  • 11
    • 85027822221 scopus 로고    scopus 로고
    • A formal series approach to averaging: exponentially small error estimates
    • (to appear). doi: 10. 3934/dcds. 2012. 32. xx
    • P. Chartier, A. Murua, J. M. Sanz-Serna, A formal series approach to averaging: exponentially small error estimates. Dyn. Syst. A (to appear). doi: 10. 3934/dcds. 2012. 32. xx.
    • Dyn. Syst. A
    • Chartier, P.1    Murua, A.2    Sanz-Serna, J.M.3
  • 12
    • 0041330504 scopus 로고    scopus 로고
    • Long-time energy conservation of numerical methods for oscillatory differential equations
    • E. Hairer, Ch. Lubich, Long-time energy conservation of numerical methods for oscillatory differential equations, SIAM J. Numer. Anal. 38, 414-441 (2000).
    • (2000) SIAM J. Numer. Anal. , vol.38 , pp. 414-441
    • Hairer, E.1    Lubich, C.2
  • 13
    • 0015960381 scopus 로고
    • On the Butcher group and general multi-value methods
    • E. Hairer, G. Wanner, On the Butcher group and general multi-value methods, Computing13, 287-303 (1974).
    • (1974) Computing , vol.13 , pp. 287-303
    • Hairer, E.1    Wanner, G.2
  • 18
    • 0033077759 scopus 로고    scopus 로고
    • Formal series and numerical integrators, part I: systems of ODEs and symplectic integrators
    • A. Murua, 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
    • 33846860618 scopus 로고    scopus 로고
    • The Hopf algebra of rooted trees, free Lie algebras and Lie series
    • A. Murua, The Hopf algebra of rooted trees, free Lie algebras and Lie series, Found. Comput. Math. 6, 387-426 (2006).
    • (2006) Found. Comput. Math. , vol.6 , pp. 387-426
    • Murua, A.1
  • 20
    • 0021660205 scopus 로고
    • The separation of motions in systems with rapidly rotating phase
    • A. I. Neishtadt, The separation of motions in systems with rapidly rotating phase, J. Appl. Math. Mech. 48, 133-139 (1984).
    • (1984) J. Appl. Math. Mech. , vol.48 , pp. 133-139
    • Neishtadt, A.I.1
  • 21
    • 0003189099 scopus 로고
    • Higher order averaging and related methods for perturbed periodic and quasi-periodic systems
    • L. M. Perko, Higher order averaging and related methods for perturbed periodic and quasi-periodic systems, SIAM J. Appl. Math. 17, 698-724 (1968).
    • (1968) SIAM J. Appl. Math. , vol.17 , pp. 698-724
    • Perko, L.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.