Finite difference discretization of the cubic Schrödinger equation

  title={Finite difference discretization of the cubic Schr{\"o}dinger equation},
  author={Georgios Akrivis},
  journal={Ima Journal of Numerical Analysis},
  • G. Akrivis
  • Published 1993
  • Mathematics
  • Ima Journal of Numerical Analysis
We analyze the discretization of an initial-boundary value problem for the cubic Schrodinger equation in one space dimension by a Crank-Nicolson-type finite difference scheme. We then linearize the corresponding equations at each time level by Newton's method and discuss an iterative modification of the linearized scheme which requires solving linear systems with the same tridiagonal matrix. We prove second-order error estimates 

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Conference Board of the Mathematical Sciences

The Policy Corntnittee was known as the Confcrcnce Organization of the Mathematical Scicnccs for a year or two before it was finally incorporated on 25 Frbruar~ 1960 in thr District of Columbia under the name Confercncc Board of the mathematical Sciences, Inc.

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  • Methds Appl. Mech. Engrg
  • 1984