674	RWTH Publication No: 1002852        2024
TITLE	A numerical method for solving the generalized tangent vector of hyperbolic systems
AUTHORS	Michael Herty, Yizhou Zhou
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 Bressan and Marson (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.
KEYWORDS	Conservative schemes, Generalized tangent vectors, Interface conditions