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arXiv · 2412.04251

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

Michael Herty·Yizhou Zhou
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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.

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Michael Herty, Yizhou Zhou. 2024-12-05. A numerical method for solving the generalized tangent vector of hyperbolic systems. https://arxiv.org/abs/2412.04251

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