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Volumn 108, Issue 2, 2007, Pages 223-262

Normal form and long time analysis of splitting schemes for the linear Schrödinger equation with small potential

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EID: 36649004371     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-007-0119-5     Document Type: Article
Times cited : (30)

References (13)
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    • Birkhoff normal form for PDEs with tame modulus
    • to appear
    • Bambusi, D., Grebert, B.: Birkhoff normal form for PDEs with tame modulus. Duke Math. J. (to appear)
    • Duke Math. J.
    • Bambusi, D.1    Grebert, B.2
  • 2
    • 0036556648 scopus 로고    scopus 로고
    • Order estimates in time of splitting methods for the nonlinear Schrödinger equation
    • 5
    • Besse C., Bidégaray B. and Descombes S. (2002). Order estimates in time of splitting methods for the nonlinear Schrödinger equation. SIAM J. Numer. Anal. 40(5): 26-40
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 26-40
    • Besse, C.1    Bidégaray, B.2    Descombes, S.3
  • 3
    • 33645522650 scopus 로고    scopus 로고
    • Conserved quantities of some Hamiltonian wave equations after full discretization
    • Cano B. (2006). Conserved quantities of some Hamiltonian wave equations after full discretization. Numer. Math. 103: 197-223
    • (2006) Numer. Math. , vol.103 , pp. 197-223
    • Cano, B.1
  • 4
    • 37449013874 scopus 로고    scopus 로고
    • Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions
    • to appear
    • Cohen, D., Hairer, E., Lubich, C.: Long-time analysis of nonlinearly perturbed wave equations via modulated Fourier expansions. Arch. Ration. Mech. Anal. (to appear)
    • Arch. Ration. Mech. Anal.
    • Cohen, D.1    Hairer, E.2    Lubich, C.3
  • 5
    • 0000670459 scopus 로고
    • Product formula algorithms for solving the time dependent Schrödinger equation
    • Raedt H. (1987). Product formula algorithms for solving the time dependent Schrödinger equation. Comput. Phys. Rep. 7: 1-72
    • (1987) Comput. Phys. Rep. , vol.7 , pp. 1-72
    • De Raedt, H.1
  • 9
    • 85095839561 scopus 로고    scopus 로고
    • Splitting methods
    • McLachlan R.I. and Quispel G.R.W. (2002). Splitting methods. Acta Numer. 11: 341-434
    • (2002) Acta Numer. , vol.11 , pp. 341-434
    • Quispel, G.R.W.1
  • 10
    • 2942627242 scopus 로고    scopus 로고
    • Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations
    • Oliver M., West M. and Wulff C. (2004). Approximate momentum conservation for spatial semidiscretizations of semilinear wave equations. Numer. Math. 97: 493-535
    • (2004) Numer. Math. , vol.97 , pp. 493-535
    • Oliver, M.1    West, M.2    Wulff, C.3
  • 12
    • 0000092377 scopus 로고    scopus 로고
    • Error bounds for exponential operator splittings
    • Jahnke T. and Lubich C. (2000). Error bounds for exponential operator splittings. BIT 40: 735-744
    • (2000) BIT , vol.40 , pp. 735-744
    • Jahnke, T.1    Lubich, C.2
  • 13
    • 0033628310 scopus 로고    scopus 로고
    • Resonant and Diophantine step sizes in computing invariant tori of Hamiltonian systems
    • Shang Z. (2000). Resonant and Diophantine step sizes in computing invariant tori of Hamiltonian systems. Nonlinearity 13: 299-308
    • (2000) Nonlinearity , vol.13 , pp. 299-308
    • Shang, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.