References
V. A. Baskakov and A. V. Popov, Wave Motion 14, 123–128 (1991).
L. Di Menza, Numer. Funct. Anal. Optim. 18, 759–775 (1997).
F. Schmidt and D. Yevick, J. Comp. Phys. 134, 96–107 (1997).
M. Ehrhardt and A. Arnold, Riv. Mat. Univ. Parma 6, 57–108 (2001).
A. Arnold, M. Ehrhardt, and I. Sofronov, Commun. Math. Sci. 1, 501–556 (2003).
I. Alonso-Mallo and N. Requera, SIAM J. Numer. Anal. 40, 134–158 (2002).
A. Schädle, Wave Motion 35, 181–188 (2002).
X. Antoine, C. Besse, and V. Mouysset, Math. Comput. 73, 1779–1999 (2004).
J.-F. Berger, M. Girod, and D. Gogny, Comput. Phys. Commun. 63, 365–374 (1991).
H. Goutte, J.-F. Berger, P. Casoly, and D. Gogny, Phys. Rev. C 71, 4316 (2005).
B. Ducomet and A. Zlotnik, Commun. Math. Sci. 4, 741–766 (2007).
A. A. Zlotnik, Sov. J. Numer. Anal. Math. Model. 6, 421–451 (1991).
U. Grenander and G. Segö, Toeplitz Forms and Their Applications (Univ. of California Press, Berkley, Los Angeles, 1958; Inostrannaya Literatura, Moscow, 1961).
W. Rudin, Real and Complex Analysis (McGraw-Hill, New York, 1974).
B. Ducomet and A. Zlotnik, Commun. Math. Sci. (2007) (in press).
Author information
Authors and Affiliations
Additional information
Published in Russian in Doklady Akademii Nauk, 2007, Vol. 413, No. 4, pp. 444–449.
Rights and permissions
About this article
Cite this article
Zlotnik, A.A., Ducomet, B. Stability of a symmetric finite-difference scheme with approximate transparent boundary conditions for the time-dependent Schrödinger equation. Dokl. Math. 75, 260–265 (2007). https://doi.org/10.1134/S1064562407020214
Received:
Issue Date:
DOI: https://doi.org/10.1134/S1064562407020214