University of Cambridge Semi-explicit Methods for Isospectral Ows Semi-explicit Methods for Isospectral Ows

University of Cambridge Runge{kutta Methods for Orthogonal and Isospectral Ows

Semi-explicit methods for isospectral flows

In this paper we propose semi-explicit schemes based on Taylor methods for the solution of the isospectral equation L′ = [B,L] for d × d real matrices L, while reproducing the isospectrality of the exact equation. Although the theoretical solution may be symmetric, the proposed schemes usually do not retain symmetry of the underlying flow. We present techniques that allow us to decrease the bre...

Numerical Solution of Isospectral

In this paper we are concerned with the problem of solving numerically isospectral ows. These ows are characterized by the diierential equation L 0 = B(L);L]; L(0) = L 0 ; where L 0 is a d d symmetric matrix, B(L) is a skew-symmetric matrix function of L and B;L] is the Lie bracket operator. We show that standard Runge{Kutta schemes fail in recovering the main qualitative feature of these ows, ...

Semi-implicit Runge-kutta Schemes for Non-autonomous Diierential Equations in Reactive Flow Computations

This paper is concerned with time-stepping numerical methods for computing stii semi-discrete systems of ordinary diierential equations for transient hyper-sonic ows with thermo-chemical nonequilibrium. The stiiness of the equations is mainly caused by the vis-cous ux terms across the boundary layers and by the source terms modeling nite-rate thermo-chemical processes. Implicit methods are need...

Stabilization of Nonholonomic Systems Using Isospectral Flows

In this paper we derive and analyze a discontinuous stabilizing feedback for a Lie algebraic generalization of a class of kinematic nonholonomic systems introduced by Brockett. The algorithm involves discrete switching between isospectral and norm-decreasing ows. We include a rigorous analysis of the convergence. 1. Introduction. In this paper we present a stabilization algorithm for a Lie