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.

翻译：本文研究一维双曲型偏微分方程一阶变分的计算问题。针对激波情形，通过构建数值方法计算Bressan与Marson（1995）提出的广义切向量演化过程，以解决该问题的主要挑战。本方法的基本策略是将守恒型数值格式与间断处切向量界面条件的新颖表达形式相结合。基于此，我们提出了一种适用于一般双曲系统的简易切向量数值计算方法。文中以Burgers方程和具有两个真非线性场的2×2双曲系统为例展示了数值计算结果。