Search Results for "numerical analysis"

...Exploit Julia's capabilities to improve computational performance of large-scale power system quasi-static simulations. The flexible modeling framework is enabled through a modular set of capabilities that enable scalable power system analysis and exploration of new analysis methods. The modularity of PowerSimulations results from the structure of the simulations enabled by the package. Simulations define a set of problems that can be solved using numerical techniques.

HomotopyContinuation.jl is a Julia package for solving systems of polynomial equations by numerical homotopy continuation. Many models in the sciences and engineering are expressed as sets of real solutions to systems of polynomial equations. We can optimize any objective whose gradient is an algebraic function using homotopy methods by computing all critical points of the objective function. An important special case is when the objective function is the euclidean distance to a given point....

Reachability analysis is concerned with computing rigorous approximations of the set of states reachable by a dynamical system. In the scope of this package are systems modeled by continuous or hybrid dynamical systems, where the dynamics change with discrete events. Systems are modeled by ordinary differential equations (ODEs) or semi-discrete partial differential equations (PDEs), with uncertain initial states, uncertain parameters or non-deterministic inputs.