# Interdisciplinary Applied Mathematics

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The advantages of the nodal analysis method for microsystem design are as follows: (i) It can solve coupled nonlinear differential equations. (ii) It is fast, reasonably accurate, flexible, and can be used for higher-level simulation of microsystems. (iii) It can perform DC, steady-state, and transient analysis. The disadvantages of the nodal analysis technique are these: (i) The approach can still be expensive for complex systems. (ii) It cannot account for all the nonlinear behavior encountered in microsystems. More details on    nodal    analysis    as    well    as    more    examples can be found    in    (Fed-

der and Jing, 1998; Vandemeer et al., 1998; Mukherjee and Fedder, 1998; Baidya and Mukherjee, 2002).

##### 17.3 Black Box Models

Black box models stem from basic ideas in system and control theory. Black box models are based on measured input-output behavior, hence the name “black box models.” Detailed results from simulations are used to construct simplified and more abstract models. The various models that fall under this category can be broadly classified into:

1. Nonlinear static models: These models use mathematical optimization, approximation, and interpolation methods for curve fitting and parameter adaptation. Table-based numerical reduced-order modeling falls in this category.

2. Linear dynamic models: These are usually formulated in the Laplace domain. The system is simulated in the time or frequency domain. Algorithms from control and system theory are used to calculate the transfer function. The response function is calculated using the convolution integral principles on the impulse function and the actual input function. If the system is complicated, random input functions may be needed to simulate the system instead of step or impulse functions. Krylov subspace techniques and moment matching methods fall under this category.

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