Numerical Solutions Of A Kind Of Nonlinear Dynamic Equations Of MEMS

In this paper, by studying the numerical solution of the thin film deflection model in MEMS, the effect of voltage on the physical state of the film is observed, therefore the critical value of the breakdown voltage is determined. Using the finite difference method,two kinds of difference schemes, with the time-space order of (1,2), (2,2) respectively,were established for the nonlinear parabolic MEMS equation, then we used the energy inequality method proving the convergence of the difference schemes and its unconditional stability. Numerical experiments show that the two schemes are effective for numerical simulation of parabolic MEMS equations; Two kinds of difference schemes, with the time-space order of (2, 2), (2, 4) respectively, were established for the nonlinear hyperbolic MEMS equation, then we used the energy inequality method proving the convergence of the difference schemes and its unconditional stability. Numerical experiments show that the two schemes are effective for numerical simulation of hyperbolic MEMS equations;For the two dimensional nonlinear hyperbolic MEMS equation, an alternating direction implicit scheme with time-space accuracy of (2, 2) was established. The convergence and unconditional stability of the scheme were proved by energy method. Numerical experiments show that the scheme are effective for numerical simulation two dimensional nonlinear hyperbolic MEMS equations. Using the above difference scheme can effectively simulate the size of the corresponding critical value voltage.