Figure 5. t=0.135, (time of beginning of gradient catastrophe), -numerical solution by scheme (3.7); - numerical solution by Lax- Friedrichs scheme

From

One Class of Stable Difference Schemes for Hyperbolic System

A.M. Blokhin, R.D. Alaev, M.U. Hudayberganov

American Journal of Numerical Analysis. 2014, 2(3), 85-89 doi:10.12691/ajna-2-3-4