Convergence Rate for the Ordered Upwind Method

Ordered Upwind Methods for Hybrid Control

We introduce a family of highly efficient (non-iterative) numerical methods for a wide class of hybrid control systems. The application of Dijkstra’s classical method to a discrete optimal trajectory problem on a network obtains the solution in O(M logM) operations. The key idea behind the method is a careful use of the direction of information propagation, stemming from the optimality principl...

$L-$ordered Fuzzifying Convergence Spaces

Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

The Upwind Differencing Method

The flux-vector and flux-difference splittings of Steger-Warming, Van Leer and Roe are tested in all possible combinations in the implicit and explicit operators that can be distinguished in implicit relaxation methods for the steady Euler and Navier-Stokes equations. The tests include one-dimensional inviscid nozzle flow, and two-dimensional inviscid and viscous shock reflection. Roe’s splitti...

Convergence of the Upwind Interface Source method for hyperbolic conservation laws

Ordered upwind methods for static Hamilton-Jacobi equations.

We introduce a family of fast ordered upwind methods for approximating solutions to a wide class of static Hamilton-Jacobi equations with Dirichlet boundary conditions. Standard techniques often rely on iteration to converge to the solution of a discretized version of the partial differential equation. Our fast methods avoid iteration through a careful use of information about the characteristi...