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BIMSA Computational Math Seminar
A numerical method for solving the generalized tangent vector
A numerical method for solving the generalized tangent vector
Organizers
Speaker
Yizhou Zhou
Time
Friday, December 19, 2025 3:00 PM - 4:00 PM
Venue
Shuangqing-B520
Online
Zoom 928 682 9093
(BIMSA)
Abstract
This talk 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.
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.