Contaminant transport in underground system usually occurs in varied flow fields and in anisotropic and heterogenous media. Because the applicability of analytical solutions is extremely limited for such conditions, and the distribution and transport of pollutants in groundwater are controlled by physics and chemistry and biology courses, which include advection, mechanical disperse, molecule s...

We develop techniques for computing the (un)stable manifold at a hyperbolic equilibrium of an analytic vector field. Our approach is based on the so-called parametrization method for invariant manifolds. A feature of this approach is that it leads to a-posteriori analysis of truncation errors which, when combined with careful management of round off errors, yields a mathematically rigorous encl...

Bounded real balanced truncation for infinite-dimensional systems is considered. This provides reduced order finite-dimensional systems that retain bounded realness. We obtain an error bound analogous to the finite-dimensional case in terms of the bounded real singular values. By using the Cayley transform a gap metric error bound for positive real balanced truncation is subsequently obtained. ...

A modification of the Balanced Stoc1insiti.c Truncation method fqr relative error model reduction is introduced. The method is based on replac~ng the truncat~on step w ~ t h a generalized s~iigular pertmbat~on approxlmatlon. The new method is shown to satisfy an infinity norm bound on the relative error between the full order and the reduced order models. The discrete time balaiiced stochastic ...