Burgers equation is a test for numerical methods

Burgers equation $u_t+uu_x=0$ reproduces some important aspects of hydrodynamic phenomena: evolution of it's solutions may lead to “strong” and “weak” breaks resembling shock waves and rarefaction waves. These types of solution were used as tests for numerical methods. Many numerical methods were compared and their influence on qualitative behaviour of numerical solution was investigated. One scheme was recommended for problems of such type.