메뉴 건너뛰기




Volumn 68, Issue 2, 2006, Pages 267-297

Mitigating the integration error in numerical simulations of Newtonian systems

Author keywords

Gauge theory; Initial value problems; Linear ordinary differential equations; Variation of parameters

Indexed keywords

ALGORITHMIC LANGUAGES; BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; ELECTROMAGNETISM; INTEGRAL EQUATIONS; LINEAR EQUATIONS;

EID: 33749433432     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1716     Document Type: Article
Times cited : (8)

References (33)
  • 1
    • 84968913951 scopus 로고    scopus 로고
    • Philosophiae naturalis principia mathematica
    • Samuel Pepys, 1687, In Newton I, Bernard Cohen I (Translator), Anne Whitman (Translator) (later edition). University of California Press: Berkeley, CA
    • Newton I. Philosophiae naturalis principia mathematica. Samuel Pepys, 1687. In The Principia: Mathematical Principles of Natural Philosophy, Newton I, Bernard Cohen I (Translator), Anne Whitman (Translator) (later edition). University of California Press: Berkeley, CA, 1999.
    • (1999) The Principia: Mathematical Principles of Natural Philosophy
    • Newton, I.1
  • 2
    • 33749445549 scopus 로고
    • Leibniz - Beyond the calculus
    • Grant H. Leibniz - beyond the calculus. Math. Semesterber 1992; 39:3-11.
    • (1992) Math. Semesterber , vol.39 , pp. 3-11
    • Grant, H.1
  • 5
    • 0012650693 scopus 로고
    • Üeber die numerische auflosung von differentialgleichungen
    • Runge C. Üeber die numerische auflosung von differentialgleichungen. Mathematische Annalen 1895; 46:167-178.
    • (1895) Mathematische Annalen , vol.46 , pp. 167-178
    • Runge, C.1
  • 6
    • 0006451452 scopus 로고
    • Beitrag zur näherungsweisen integration totaler differentialgleichungen
    • Kutta W. Beitrag zur näherungsweisen integration totaler differentialgleichungen. Zeitschr. fur Math. u. Phys. 1901; 46:435-453.
    • (1901) Zeitschr. Fur Math. U. Phys. , vol.46 , pp. 435-453
    • Kutta, W.1
  • 7
    • 0003015990 scopus 로고
    • Über die numcrisehe integration yon differentialgleiehungen
    • Nyström EJ. Über die numcrisehe integration yon differentialgleiehungen. Acta Soc. Sci. Fennica 1925; 50:5.
    • (1925) Acta Soc. Sci. Fennica , vol.50 , pp. 5
    • Nyström, E.J.1
  • 8
    • 25544464192 scopus 로고
    • Une amëtlioration de ia méthode de Runge-Kutta-Nyström pour la résolution numérique des équations différentielles du premier ordre
    • Huťa A. Une amëtlioration de ia méthode de Runge-Kutta-Nyström pour la résolution numérique des équations différentielles du premier ordre. Acta Mathematica Universitatis Comenianae 1965; 1:21-24.
    • (1965) Acta Mathematica Universitatis Comenianae , vol.1 , pp. 21-24
    • Huťa, A.1
  • 10
    • 0039179842 scopus 로고
    • An eighth order Runge-Kutta process with eleven function evaluations per step
    • Curtis AR. An eighth order Runge-Kutta process with eleven function evaluations per step. Numerische Mathematik 1970; 16:268-277.
    • (1970) Numerische Mathematik , vol.16 , pp. 268-277
    • Curtis, A.R.1
  • 14
    • 0344181400 scopus 로고    scopus 로고
    • Recherches sur la question des inegalites du mouvement de Saturne et de Jupiter, sujet propose pour le prix de l'annee
    • For modern edition see: Euler L. Opera mechanica et astronomica, Birkhauser-Verlag: Switzerland
    • Euler L. Recherches sur la question des inegalites du mouvement de Saturne et de Jupiter, sujet propose pour le prix de l'annee. Piece qui a remporte le prix de l'academie royale des sciences, 1748. For modern edition see: Euler L. Opera mechanica et astronomica, Birkhauser-Verlag: Switzerland, 1999.
    • (1999) Piece Qui a Remporte Le Prix De L'academie Royale Des Sciences, 1748
    • Euler, L.1
  • 15
    • 33749447445 scopus 로고    scopus 로고
    • Theoria motus Lunae exhibens omnes ejus inaequalitates etc
    • St. Petersburg: Russia, 1753. Euler L. Opera mechanica et astronomica. (modern edition). Birkhauser-Verlag: Switzerland
    • Euler L. Theoria motus Lunae exhibens omnes ejus inaequalitates etc. Impensis Academiae Imperialis Scientarum Petropolitanae. St. Petersburg: Russia, 1753. Euler L. Opera mechanica et astronomica. (modern edition). Birkhauser-Verlag: Switzerland, 1999.
    • (1999) Impensis Academiae Imperialis Scientarum Petropolitanae
    • Euler, L.1
  • 19
    • 0345043930 scopus 로고    scopus 로고
    • Implicit gauge symmetry emerging in the n-body problem of celestial mechanics
    • Astro-ph/0212245
    • Efroimsky M. Implicit gauge symmetry emerging in the n-body problem of celestial mechanics. Astro-ph/0212245, 2002.
    • (2002)
    • Efroimsky, M.1
  • 20
    • 0345581673 scopus 로고    scopus 로고
    • Gauge symmetry of the n-body problem in the Hamilton-Jacobi approach
    • Efroimsky M, Goldreich P. Gauge symmetry of the n-body problem in the Hamilton-Jacobi approach. Journal of Mathematical Physics 2003; 44:5958-5977.
    • (2003) Journal of Mathematical Physics , vol.44 , pp. 5958-5977
    • Efroimsky, M.1    Goldreich, P.2
  • 21
    • 1542366376 scopus 로고    scopus 로고
    • Gauge symmetry of the n-body problem of celestial mechanics
    • Efroimsky M, Goldreich P. Gauge symmetry of the n-body problem of celestial mechanics. Astronomy and Astrophysics 2004; 415:1187-1199.
    • (2004) Astronomy and Astrophysics , vol.415 , pp. 1187-1199
    • Efroimsky, M.1    Goldreich, P.2
  • 22
    • 12744265266 scopus 로고    scopus 로고
    • j2-perturbed motion using mean non-osculating orbital elements
    • j2-perturbed motion using mean non-osculating orbital elements. Celestial Mechanics and Dynamical Astronomy 2004; 90:289-306.
    • (2004) Celestial Mechanics and Dynamical Astronomy , vol.90 , pp. 289-306
    • Gurfil, P.1
  • 26
    • 0003564548 scopus 로고    scopus 로고
    • (4th edn). Pearson Education International: New York
    • Ogata K. Modern Control Engineering (4th edn). Pearson Education International: New York, 2002.
    • (2002) Modern Control Engineering
    • Ogata, K.1
  • 29
    • 0345043927 scopus 로고    scopus 로고
    • The method of variation of parameters and multiple time scales in orbital mechanics
    • Newman WI, Efroimsky M. The method of variation of parameters and multiple time scales in orbital mechanics. Chaos 2003; 13:476-485.
    • (2003) Chaos , vol.13 , pp. 476-485
    • Newman, W.I.1    Efroimsky, M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.