The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x＇（t） = g（x（t）,x（qt））（q∈ （0, 1）, t 〉 0） is investigated. A sufficient condition is presented to ensure that the...The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x＇（t） = g（x（t）,x（qt））（q∈ （0, 1）, t 〉 0） is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.展开更多
In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the loca...In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.展开更多
In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-...In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-dimensional (1-D) PIN diode structure simulation achieved by solving the drift diffusion model (DDM). Backward Euler algorithm is used for the discretization of the proposed model. The aim is to accomplish time-domain integration. Also, finite different method (FDM) is considered to achieve space-Domain mesh. We introduced an iterative scheme to solve the obtained matrix systems, which combines the Gummel’s iteration with an efficient direct numerical UMFPACK method. The obtained solutions of the proposed algorithm provide the time and space distribution of the unknown functions like electrostatic potential and carrier’s concentration for the PIN diode. As second case, the finite-difference time-domain (FDTD) technique is adopted to analyze the entire 3-D structure of the stripline circuit including the lumped element PIN diode. The microwave circuit is located in an unbounded medium, requiring absorbing boundaries to avoid nonphysical reflections. Active device results were presented and show a good agreement with other reference. Electromagnetic results are qualitatively in agreement with other results obtained using SILVACO-TCAD.展开更多
基金This work is supported by the National Natural Science Foundation of China(Grant No.10571147).
文摘The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x＇（t） = g（x（t）,x（qt））（q∈ （0, 1）, t 〉 0） is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.
基金supported by National Natural Science Foundation of China (Grant No. 11571128)
文摘In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method.
文摘In this work, we present a numerical model to solve the drift diffusion equations coupled with electromagnetic model, where all simulations codes are implemented using MATLAB code software. As first, we present a one-dimensional (1-D) PIN diode structure simulation achieved by solving the drift diffusion model (DDM). Backward Euler algorithm is used for the discretization of the proposed model. The aim is to accomplish time-domain integration. Also, finite different method (FDM) is considered to achieve space-Domain mesh. We introduced an iterative scheme to solve the obtained matrix systems, which combines the Gummel’s iteration with an efficient direct numerical UMFPACK method. The obtained solutions of the proposed algorithm provide the time and space distribution of the unknown functions like electrostatic potential and carrier’s concentration for the PIN diode. As second case, the finite-difference time-domain (FDTD) technique is adopted to analyze the entire 3-D structure of the stripline circuit including the lumped element PIN diode. The microwave circuit is located in an unbounded medium, requiring absorbing boundaries to avoid nonphysical reflections. Active device results were presented and show a good agreement with other reference. Electromagnetic results are qualitatively in agreement with other results obtained using SILVACO-TCAD.
