Numerical Analysis of the One-Dimensional Nonlinear Boundary Value Problem that Modeling an Electrostatic NEMS by Two-Sided Approximations Method

O. Konchakovska, M. Sidorov

Department of Applied Mathematics, Faculty of Information and Analytical Technologies and Managment,
Kharkiv National University of Radio Electronics,
61166, Kharkiv, Ukraine

Received 17 May, 2020; accepted in revised form 10 November, 2020

Abstract: The problem of numerical analysis of a nanoelectromechanical system, whose mathematical model is the first boundary value problem for a nonlinear one-dimensional elliptic equation, has been considered. An algorithm for obtaining two-sided approximations to a unique positive solution of the problem has been constructed using the method of successive approximations. The work of the proposed method is demonstrated by a series of computational experiments.

c? 2020 European Society of Computational Methods in Sciences and Engineering

Keywords: two-sided approach method, Green’s functions method, strongly invariant cone
segment, heterotone operator, nanoelectromechanical system
Mathematics Subject Classification: 34B15; 34B18


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