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Volume 17, Issue 2
A Leap Frog Finite Difference Scheme for a Class of Nonlinear Schrödinger Equations of High Order

Wen-Ping Zeng

J. Comp. Math., 17 (1999), pp. 133-138.

Published online: 1999-04

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  • 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. 

  • Keywords

High order nonlinear Schrödinger equation, Leap-Frog difference scheme, Convergence.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@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} }
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. 

Zeng , Wen-Ping. (1999). A Leap Frog Finite Difference Scheme for a Class of Nonlinear Schrödinger Equations of High Order. Journal of Computational Mathematics. 17 (2). 133-138. doi:
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