# Interdisciplinary Applied Mathematics

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value are neglected.

The advantages of this method are: (i) Reduction in computational effort. (ii) A wide variety of physical phenomena encountered in microsystems, including dissipation, can be modeled. (iii) The accuracy can be improved by taking more moments at each node. (iv) Static, steady-state, and transient analysis can be performed. The disadvantages of this approach are: (i) It is applicable for linear dynamical systems only. (ii) It is inefficient if the number of inputs is large. (iii) It is not stable for higher-order approximations. (iv) It is computationally expensive for each expansion point.

The multinode moment matching (MMM) method (Ismail, 2002) is an extension of the single point moment matching (SMM) method and has much better efficiency than to the SMM technique. The MMM technique simultaneously matches the moments at several nodes of a circuit using explicit moment matching around s = 0. MMM requires a smaller computational effort, since only (q + 1) moments are required (see (Ismail, 2002) for details). MMM is numerically stable, as the higher powers are not used in the expansion, avoiding truncation errors.

17.3.3 Nonlinear Dynamic Models

Nonlinear dynamic models are frequently encountered in microsystems. Linearizing the nonlinear equations and using reduced-order methods like the linear Krylov subspace method based on a Lanczos process or other linear basis function techniques may not be sufficient to capture the nonlinear behavior of the system. Arnoldi-based Krylov subspace methods (Chen and White, 2000) and the trajectory piecewise linear approach (Rewienski and White, 2001) and its modifications are found to work better for nonlinear systems. These techniques are summarized in this section.

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