TY - JOUR T1 - A Leap Frog Finite Difference Scheme for a Class of Nonlinear Schrödinger Equations of High Order AU - Zeng , Wen-Ping JO - Journal of Computational Mathematics VL - 2 SP - 133 EP - 138 PY - 1999 DA - 1999/04 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9088.html KW - High order nonlinear Schrödinger equation, Leap-Frog difference scheme, Convergence. AB -

In this paper, the periodic initial value problem for the following class of nonlinear schrödinger equation of high order $$i \frac{∂u}{∂t} + (–1)^m \frac{∂^m}{∂x^m} \Bigg( a(x) \frac{∂^mu}{∂x^m} \Bigg) + β (x)q(|u|^2)u + f (x; t)u = g(x; t)$$ is considered. A leap-frog finite difference scheme is given, and convergence and stability is proved. Finally, it is shown by a numerical example that numerical result is coincident with theoretical result.