Numerical Algorithms

, Volume 82, Issue 1, pp 223–243 | Cite as

A new FDTD scheme for Maxwell’s equations in Kerr-type nonlinear media

  • Hongen Jia
  • Jichun LiEmail author
  • Zhiwei Fang
  • Ming Li
Original Paper


In this paper, we develop a totally new direct finite difference solver for solving the Maxwell’s equations in Kerr-type nonlinear media. The direct method is free of iteration error and more efficient than the classic iteration method. We also prove the continuous stability for the Kerr model and the discrete stability for the proposed scheme. Extensive numerical results are presented to validate our analysis.


Maxwell’s equations FDTD method Kerr medium Soliton Nonlinear media 


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of MathematicsTaiyuan University of TechnologyTaiyuanChina
  2. 2.Department of Mathematical SciencesUniversity of Nevada Las VegasLas VegasUSA

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