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On the convergence of a difference scheme for coupled nonlinear Schrödinger equations

✍ Scribed by Zhi-zhong Sun; Dan-dan Zhao

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
394 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this article, a finite difference scheme for coupled nonlinear Schrödinger equations is studied. The existence of the difference solution is proved by Brouwer fixed point theorem. With the aid of the fact that the difference solution satisfies two conservation laws, the finite difference solution is proved to be bounded in the discrete L ∞ norm. Then, the difference solution is shown to be unique and second order convergent in the discrete L ∞ norm. Finally, a convergent iterative algorithm is presented.

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