A numerical method for solving the generalized tangent vector of hyperbolic systems

UpSpace Institutional Repository (University of Pretoria)

Abstract

This work is concerned with the computation of the first-order variation for one-dimensional hyperbolic partial differential equations. In the case of shock waves the main challenge is addressed by developing a numerical method to compute the evolution of the generalized tangent vector introduced by [A. Bressan and A. Marson, Comm. Part. Diff. Eqs., 20(9-10):1491-1552, 1995]. Our basic strategy is to combine the conservative numerical schemes and a novel expression of the interface conditions for the tangent vectors along the discontinuity. Based on this, we propose a simple numerical method to compute the tangent vectors for general hyperbolic systems. Numerical results are presented for Burgers' equation and a 2 X 2 hyperbolic system with two genuinely nonlinear fields.

Authors 1

1. Michaël Herty Aachen Chair in Numerical Analysis

   RWTH Aachen University

   Affiliation as printed

   Chair in Numerical Analysis , IGPM , RWTH Aachen University , Templergraben, 55 , D-52062 Aachen , Germany