Optimal third-kind Chebyshev collocation algorithm for solving beam-type micro- and nanoscale BVPs

Document Type : Research Article

Authors

1 Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt

2 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11341, Egypt

Abstract

In this paper, we develop a numerical scheme for solving nonlinear boundary value problems (BVPs) arising in cantilever-type micro-electromechanical (MEMS) and nano-electromechanical (NEMS) systems. The method is based on a novel third-kind Chebyshev collocation approach. We derive an operational matrix of derivatives using shifted third-kind Chebyshev polynomials, which enables efficient spectral approximations of the governing equations. Numerical experiments confirm the accuracy and efficiency of the proposed method in handling the nonlinearities present in MEMS/NEMS actuator models.

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Journal of Mathematical Modeling
Volume 13, Issue 4
December 2025
Pages 883-898

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