@Article{JCM-17-133, author = {Zeng , Wen-Ping}, title = {A Leap Frog Finite Difference Scheme for a Class of Nonlinear Schrödinger Equations of High Order}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {2}, pages = {133--138}, abstract = {

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. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9088.html} }