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Volumn 40, Issue 4, 2002, Pages 1281-1310

A Wigner-measure analysis of the Dufort-Frankel scheme for the Schrödinger equation

Author keywords

Finite difference scheme; Schr dinger equation; Semiclassical limit; Wigner measure

Indexed keywords

CONTINUUM MECHANICS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENCE EQUATIONS; FINITE DIFFERENCE METHOD; WAVELET TRANSFORMS;

EID: 0141645582     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142900381734     Document Type: Article
Times cited : (44)

References (19)
  • 3
    • 0002375163 scopus 로고    scopus 로고
    • Quantum hydrodynamics, Wigner transforma and the classical limit
    • [GM]
    • [GM] I. GASSER AND P A. MARKOWICH, Quantum hydrodynamics, Wigner transforma and the classical limit, Asymptot. Anal, 14 (1997), pp. 97-116.
    • (1997) Asymptot. Anal , vol.14 , pp. 97-116
    • Gasser, I.1    Markowich, P.A.2
  • 7
    • 0041730125 scopus 로고    scopus 로고
    • On convergence and stability of the explicit difference method for solution of nonlinear Schrödinger equations
    • [IR]
    • [IR] F. IVANAUSKAS AND M. RADZ̃IŪNAS, On convergence and stability of the explicit difference method for solution of nonlinear Schrödinger equations, SIAM J. Numer. Anal., 36 (1999), pp. 1466-1481.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 1466-1481
    • Ivanauskas, F.1    Radz̃iunas, M.2
  • 8
    • 0000953038 scopus 로고
    • The behavior of solutions of the NLS equation in the semiclassical limit
    • [JLL], Plenum Press, New York, London
    • [JLL] S. JIN, C. D. LEVERMORE, AND D. W. MCLAUGHLIN, The behavior of solutions of the NLS equation in the semiclassical limit, in Singular Limits of Dispersive Waves, Plenum Press, New York, London, 1994, pp. 235-255.
    • (1994) Singular Limits of Dispersive Waves , pp. 235-255
    • Jin, S.1    Levermore, C.D.2    McLaughlin, D.W.3
  • 10
    • 0001314058 scopus 로고
    • Sur les mesures de Wigner
    • [LP]
    • [LP] P. L. LIONS AND T. PAUL, Sur les mesures de Wigner, Rev. Mat. Iberoamericana, 9 (1993), pp. 553-618.
    • (1993) Rev. Mat. Iberoamericana , vol.9 , pp. 553-618
    • Lions, P.L.1    Paul, T.2
  • 11
    • 0039815285 scopus 로고
    • The theory of bicharacteristics for difference schemes
    • [M1]
    • [M1] V. MASLOV, The theory of bicharacteristics for difference schemes, Uspekhi Mat. Nauk, 23 (1968), p. 243.
    • (1968) Uspekhi Mat. Nauk , vol.23 , pp. 243
    • Maslov, V.1
  • 13
    • 0041001943 scopus 로고
    • The characteristics of pseudo-differential operators and difference schemes
    • [M3]
    • [M3] V. MASLOV, The characteristics of pseudo-differential operators and difference schemes, Actes Cong. Intern. Math., 2 (1970), pp. 755-769.
    • (1970) Actes Cong. Intern. Math. , vol.2 , pp. 755-769
    • Maslov, V.1
  • 14
    • 36449006348 scopus 로고
    • A Wigner function approach to semiclassical limits: Electrons in a periodic potential
    • [MMP]
    • [MMP] P. A. MARKOWICH, N. J. MAUSER, AND F. POUPAUD, A Wigner function approach to semiclassical limits: Electrons in a periodic potential, J. Math. Phys., 35 (1994), pp. 1066-1094.
    • (1994) J. Math. Phys. , vol.35 , pp. 1066-1094
    • Markowich, P.A.1    Mauser, N.J.2    Poupaud, F.3
  • 15
    • 0011569744 scopus 로고    scopus 로고
    • The pseudo-differential approach to finite differences revisited
    • [MP]
    • [MP] P. A. MARKOWICH AND F. POUPAUD, The pseudo-differential approach to finite differences revisited, Calcolo, 36 (1999), pp. 161-186.
    • (1999) Calcolo , vol.36 , pp. 161-186
    • Markowich, P.A.1    Poupaud, F.2
  • 16
    • 0033480955 scopus 로고    scopus 로고
    • Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit
    • [MPP]
    • [MPP] P. A. MARKOWICH, P. PIETRA, AND C. POHL, Numerical approximation of quadratic observables of Schrödinger-type equations in the semi-classical limit, Numer, Math., 81 (1999), pp. 595-630.
    • (1999) Numer. Math. , vol.81 , pp. 595-630
    • Markowich, P.A.1    Pietra, P.2    Pohl, C.3
  • 17
    • 84974050752 scopus 로고
    • H-measures: A new approach for studying homogenization, oscillations and concentration effects in partial differential equations
    • [T]
    • [T] L. TARTAR., H-measures: A new approach for studying homogenization, oscillations and concentration effects in partial differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 115 (1990), pp. 193-230.
    • (1990) Proc. Roy. Soc. Edinburgh Sect. A , vol.115 , pp. 193-230
    • Tartar, L.1
  • 18
    • 0011495032 scopus 로고    scopus 로고
    • Dufort-Frankel-type methods for linear and nonlinear Schrödinger equations
    • [W]
    • [W] L. WU, Dufort-Frankel-type methods for linear and nonlinear Schrödinger equations, SIAM J. Numer, Anal., 33 (1996), pp. 1526-1533.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1526-1533
    • Wu, L.1
  • 19
    • 33745014742 scopus 로고
    • On the quantum correction for the thermodynamic equilibrium
    • [Wi]
    • [Wi] E. WIGNER, On the quantum correction for the thermodynamic equilibrium, Phys. Rev. II, 40 (1932), pp. 749-759.
    • (1932) Phys. Rev. II , vol.40 , pp. 749-759
    • Wigner, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.