An Etymological Dictionary of Astronomy and Astrophysics

The combination of a → partial differential equation and a → piecewise constant → initial condition. The Riemann problem is a basic tool in a number of numerical methods for wave propagation problems. The canonical form of the Riemann problem is:

∂u/∂t + ∂f(u)/∂x = 0, x ∈ R, t > 0, u(x,0) = u_l if x < 0, and
u(x,0) = u_r if x > 0 .

See also: → Riemann’s geometry; → problem.