Метод двобічних наближень у чисельному аналізі одновимірної мікроелектромеханічної системи під дією зовнішнього тиску

Abstract

The paper considers the numerical analysis of an electrostatic microelectromechanical system under the influence of external pressure. The first boundary value problem for a nonlinear one-dimensional elliptic equation represents the mathematical model of this process. To solve this problem, we have constructed an algorithm that obtains two-sided approximations to the unique positive solution of the problem using the method of successive approximations. The method of successive approximations is used to solve nonlinear equations by iteratively computing a sequence of approximations until a desired level of accuracy is achieved. To demonstrate the effectiveness of our proposed method, we conducted a series of computational experiments.