Backward Differentiation Approximations of Nonlinear Differential/Algebraic Systems

Backward Differentiation Approximations of Nonlinear Differential/Algebraic Systems

Finite difference approximations of dynamical systems modelled by nonlinear, semiexplicit, differential/algebraic equations are analyzed. Convergence for the backward differentiation method is proved for index two and index three problems when the numerical initial values obey certain constraints. The appropriate asymptotic convergence rates and the leading error terms are determined.

Observability and Forward-Backward Observability of Discrete-Time Nonlinear Systems

In this paper, we study the observability properties of nonlinear discrete time systems. Two types of contributions are given. First, we present observability criteria in terms of appropriate codistributions. For particular, but significant, classes of systems we provide criteria that require only a finite number of computations. Then, we consider invertible systems (which includes discrete-tim...

Convergence of Diffusive Bgk Approximations for Nonlinear Strongly Parabolic Systems

Linear approximations of nonlinear FIR systems for separable input processes

Nonlinear systems can be approximated by linear time-invariant (LTI) models in many ways. Here, LTI models that are optimal approximations in the meansquare error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is prese...

Weakly Nonlinear-dissipative Approximations of Hyperbolic-parabolic Systems with Entropy

Hyperbolic-parabolic systems have spatially homogenous stationary states. When the dissipation is weak, one can derive weakly nonlinear-dissipative approximations that govern perturbations of these constant states. These approximations are quadratically nonlinear. When the original system has an entropy, the approximation is formally dissipative in a natural Hilbert space. We show that when the...