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

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.

Keywords:

Third-kind Chebyshev polynomials , collocation method , MEMS/NEMS actuators , Nonlinear boundary value problems