Electronic Research Archive
The special issue of algebraic representation theory
Xueqing Chen, University of Wisconsin-Whitewater, USA email@example.com
Min Huang, Research Fellow, University of Hong Kong, China; Sun Yat-sen University (Zhuhai Campus), China firstname.lastname@example.org
Fang Li, Zhejiang University, China email@example.com
In this paper, we consider a kind of efficient finite difference methods (FDMs) for solving the nonlinear Helmholtz equation in the Kerr medium. Firstly, by applying several iteration methods, we linearize the nonlinear Helmholtz equation in several different ways. Then, based on the resulted linearized problem at each iterative step, by rearranging the Taylor expansion and using the ADI method, we deduce a kind of new FDMs, which also provide a route to deal with the problem with discontinuous coefficients.Finally, some numerical results are presented to validate the efficiency of the proposed schemes, and to show that our schemes perform with much higher accuracy and better convergence compared with the classical ones.
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