Numerical simulation of porous silicon morphology using a monotone iterative method

Flores, Salvador Saucedo; Jerez, Silvia

doi:10.1016/j.cnsns.2018.09.028

Cited by 3 publications

(1 citation statement)

References 37 publications

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“…As for the continuous case, the numerical monotone iterative methods require the knowledge of upper and lower solutions in order to generate two monotone sequences that converge to the solution of the problems under investigation. Numerical techniques of this nature have been employed to solve the multidimensional semiconductor Poisson equation [8], to simulate quantumcorrected energy transport models [9], to study numerically the solutions of parabolic problems with time delays [10], to investigate two-dimensional simulation of submicron MOSFETs [11], to provide numerical analysis of coupled systems of nonlinear parabolic equations [12], and to simulate porous silicon morphologies [13]. In various of these reports and many other articles which employ discrete monotone iterative approaches, this methodology has been used to prove the existence and uniqueness of solutions, as well as to investigate the numerical efficiency of the computational algorithms.…”

Section: Introductionmentioning

confidence: 99%

Discrete monotone method for space-fractional nonlinear reaction–diffusion equations

2019

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A discrete monotone iterative method is reported here to solve a space-fractional nonlinear diffusion-reaction equation. More precisely, we propose a Crank-Nicolson discretization of a reaction-diffusion system with fractional spatial derivative of the Riesz type. The finite-difference scheme is based on the use of fractional-order centered differences, and it is solved using a monotone iterative technique. The existence and uniqueness of solutions of the numerical model are analyzed using this approach, along with the technique of upper and lower solutions. This methodology is employed also to prove the main numerical properties of the technique, namely, the consistency, stability, and convergence. As an application, the particular case of the space-fractional Fisher's equation is theoretically analyzed in full detail. In that case, the monotone iterative method guarantees the preservation of the positivity and the boundedness of the numerical approximations. Various numerical examples are provided to illustrate the validity of the numerical approximations. More precisely, we provide an extensive series of comparisons against other numerical methods available in the literature, we show detailed numerical analyses of convergence in time and in space against fractional and integer-order models, and we provide studies on the robustness and the numerical performance of the discrete monotone method. MSC: Primary 65M06; secondary 35K15; 35K55; 35K57

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Section: Introductionmentioning

confidence: 99%

Discrete monotone method for space-fractional nonlinear reaction–diffusion equations

2019

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Asymptotic behavior of reaction–advection–diffusion population models with Allee effect

Jerez

Verdugo

2020

Math Methods in App Sciences

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In this work, a qualitative analysis is carried out for reaction–advection–diffusion (RAD) systems modeling the interactions between two species with Allee effect. In particular, we study different scenarios: mutualism, competition, and a predator–prey relationship in order to investigate the survival or extinction of both populations. Global existence and uniqueness of positive solutions of the proposed RAD problems are demonstrated. Equilibrium states and asymptotic behavior of solutions are obtained using the monotone method and the upper and lower solutions technique. Numerical simulations by a Crank–Nicolson monotone iterative method of the different asymptotic solution dynamics are shown to illustrate our theoretical results.

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Development of Multitextures on the Basis of Porous Silicon for High Performance Photoelectric Converters

Yerokhov

Druzhinin

Khoverko

et al. 2019

2019 International Conference on Information and Telecommunication Technologies and Radio Electronics (UkrMiCo)

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Numerical simulation of porous silicon morphology using a monotone iterative method

Cited by 3 publications

References 37 publications

Discrete monotone method for space-fractional nonlinear reaction–diffusion equations

Discrete monotone method for space-fractional nonlinear reaction–diffusion equations

Asymptotic behavior of reaction–advection–diffusion population models with Allee effect

Development of Multitextures on the Basis of Porous Silicon for High Performance Photoelectric Converters

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