eISSN:
 2688-1594

Electronic Research Archive

Specail issue on vertex algebras, lie algebras, and related topics

Ching Hung Lam, Academia Sinica, Taiwan chlam@math.sinica.edu.tw

Haisheng Li, Rutgers University, Camden, USA hli@camden.rutgers.edu

Qiang Mu, Harbin Normal University, China qmu520@gmail.com

Solvability of the matrix equation AX2=B with semi-tensor productSpecial Issues
Jin Wang Jun-E Feng and Hua-Lin Huang
2020,  doi: 10.3934/era.2020114 +[Abstract](15)+[HTML](11) +[PDF](400.64KB)
Abstract:

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.

Classification of finite irreducible conformal modules over Lie conformal algebra W(a,b,r)Special Issues
Wenjun Liu, Yukun Xiao,  and Xiaoqing Yue
2020,  doi: 10.3934/era.2020123 +[Abstract](15)+[HTML](11) +[PDF](306.09KB)
Abstract:

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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