Methods for the Numerical Solution of the Nonlinear Schroedinger Equation

@inproceedings{SanzSerna2010MethodsFT,
  title={Methods for the Numerical Solution of the Nonlinear Schroedinger Equation},
  author={Jes{\'u}s Maŕıa Sanz-Serna},
  year={2010}
}
Optimal L2 rates of convergence are established for several fully-discrete schemes for the numerical solution of the nonlinear Schroedinger equation. Both finite differences and finite elements are considered for the discretization in space, while the integration in time is treated either by the leap-frog technique or by a modified Crank-Nicolson procedure, which generalizes the one suggested by Delfour, Fortin and Payne and possesses two useful conserved quantities. 

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View 1 Excerpt
Highly Influenced

References

Publications referenced by this paper.
Showing 1-10 of 18 references

A method for the integration in time of certain partial differential equations,

J. M. Sanz-Serna, V. S. Manoranjan
J. Comput. Phys., • 1983
View 6 Excerpts
Highly Influenced

Finite-difference solution of a nonlinear Schroedinger equation,"

M. Delfour, M. Fortin, G. Payne
Comput. Phys., • 1981
View 6 Excerpts
Highly Influenced

J

D. F. Griffiths, A. R. Mitchel
Ll. Morris, A Numerical Study of the Nonlinear Schroedinger Equation, Department of Mathematics, University of Dundee, Report NA/52, May • 1982
View 6 Excerpts
Highly Influenced

The nonlinear Schroedinger equation" in Contemporary Developments in Continuum Mechanics and Partial Differential Equations (G

W. A. Strauss
M. de la Penha and L. A. Medeiros, Eds.), North-Holland, New York, • 1978
View 7 Excerpts
Highly Influenced

Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media,

V. E. Zakharov, A. B. Shabat
Soviet Phys. JETP, v. 34,1972, • 1972
View 3 Excerpts
Highly Influenced

Lopez-Marcos, Integración Numérica de la Ecuación de Schroedinger no lineal

J C.
M.Sc. thesis, • 1983
View 1 Excerpt

W . A . Strauss , " The nonlinear Schroedinger equation " in Contemporary Developments in Continuum Mechanics and Partial Differential Equations ( G . M . de la Penha and L

. A. Medeiros
1983

Convergence of methods for the numerical solution of the Korteweg-de Vries equation

Kuo Pen-Yu, J. M. Sanz-Serna
IMA J. Numer. Anal., • 1981
View 1 Excerpt

Jr

D. N. Arnold, J. Douglas
& V. Thomée, "Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable," Math. Comp., v. 36, • 1981
View 1 Excerpt

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