标题： 求解双曲系统广义切向量的数值方法 显示英文标题

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

摘要： 这项工作涉及一维双曲偏微分方程的一阶变分计算。 在冲击波的情况下，通过开发一种数值方法来计算Bressan和Marson（1995）引入的广义切向量的演化来解决主要挑战。 我们的基本策略是结合保守数值格式和沿不连续性处切向量的新界面条件表达式。 基于此，我们提出了一种简单的数值方法来计算一般双曲系统的切向量。 给出了Burgers方程和一个具有两个真正非线性场的2 x 2双曲系统的数值结果。 显示英文摘要

摘要： 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.