  The paper deals with solving first-order quasilinear partial differential
equations in an online simulation environment, such as Simulink, utilizing the
well-known and well-recommended method of characteristics. Compared to the
commonly applied space discretization methods on static grids, the
characteristics-based approach provides better numerical stability. Simulink
subsystem implementing the method of characteristics is developed. It employs
Simulink's built-in solver and its zero-crossing detection algorithm to perform
simultaneous integration of a pool of characteristics as well as to create new
characteristics dynamically and discard the old ones. Numerical accuracy of the
solution thus obtained is established. The subsystem has been tested on a
full-state feedback example and produced better results than the space
discretization-based "method of lines". The implementation is available for
download and can be used in a wide range of models.
