In this paper, a numerical approach is suggested to find a semi-analytical solution for the common nonlinear boundary value problems (BVPs) of cantilever-type micro-electromechanical system (MEMS) and nano-electromechanical system (NEMS) with a set of model parameters. The nonlinear BVPs that are studied involve the states of the single and double cantilever-shaped beams under the influence of Casimir and Van der Waals force for proper distances of separation. The method is based upon an integral operator that is formed considering Green’s function connected with the execution of Picard’s or Mann’s fixed point schemes. The numerical results for different cases of beam are presented and compared with those obtained by previous works to show the applicability, efficiency, and high accuracy of the suggested method.

中文翻译：

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一种用于分析梁式机电执行器吸合动力学的定点迭代方法

在本文中，提出了一种数值方法来寻找悬臂式微机电系统 (MEMS) 和纳米机电系统 (NEMS) 的常见非线性边界值问题 (BVP) 的半解析解，其中包含一组模型参数。所研究的非线性 BVP 涉及在 Casimir 和范德华力的影响下单双悬臂梁的状态，以获得适当的分离距离。该方法基于积分算子，该算子考虑与皮卡德或曼定点方案的执行相关的格林函数而形成。给出了不同梁情况下的数值结果，并与先前工作获得的数值结果进行了比较，以表明所建议方法的适用性、效率和高精度。