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 - <p style="text-align: justify;">In this paper, the periodic initial value problem for the following class of nonlinear schrödinger equation of high order $$i&nbsp;\frac{∂u}{∂t} + (–1)^m \frac{∂^m}{∂x^m} \Bigg( a(x) \frac{∂^mu}{∂x^m} \Bigg) +&nbsp;β(x)q(|u|^2)u + f (x; t)u = g(x; t)$$ 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.&nbsp;</p>