A semi-discrete model and its approach to a solution for a wide moving jam in traffic flow

► The Lagrange coordinate is used to formulate a continuum traffic flow model. ► This also gives a semi-discrete model including a car-following model. ► A wide moving jam is analytically derived in the continuum model. ► A similar solution is derived through simulation in the discrete model. ► We show the convergence of the latter solution to the former.