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Special issue on stability and complexity of differential systems

David Cheban, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China; State University of Moldova, Faculty of Mathematics and Informatics, Department of Mathematics, A. Mateevich Street 60, MD--2009 Chişinău, Moldova cheban@usm.md
Wen Huang, CAS Wu Wen-Tsun Key Laboratory of Mathematics, and Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China wenh@mail.ustc.edu.cn
Zhenxin Liu, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China zxliu@dlut.edu.cn

Averaging principle on infinite intervals for stochastic ordinary differential equationsSpecial Issues
David Cheban   and Zhenxin Liu
2021,  doi: 10.3934/era.2021014 +[Abstract](15)+[HTML](11) +[PDF](387.01KB)
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.

Ergodic measures of intermediate entropy for affine transformations of nilmanifoldsSpecial Issues
Wen Huang, Leiye Xu,  and Shengnan Xu
2021,  doi: 10.3934/era.2021015 +[Abstract](15)+[HTML](11) +[PDF](313.83KB)
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.

Instability and bifurcation of a cooperative system with periodic coefficientsSpecial Issues
Tian Hou, Yi Wang and Xizhuang Xie
2021,  doi: 10.3934/era.2021026 +[Abstract](15)+[HTML](11) +[PDF](807.77KB)
Abstract:
Simultaneous recovery of surface heat flux and thickness of a solid structure by ultrasonic measurementsSpecial Issues
Youjun Deng, Hongyu Liu, Xianchao Wang, Dong Wei and Liyan Zhu
2021,  doi: 10.3934/era.2021027 +[Abstract](15)+[HTML](11) +[PDF](525.34KB)
Abstract:

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