We illustrate recently proposed large time step method for hyperbolic conservation laws. In the scalar case, it was proved earlier that if the approximate solutions converge boundedly, then they converge to the entropy solution. The main goal of this paper is to consider the large time step method for several systems of hyperbolic conservation laws. We compute approximate solutions to Riemann problems for three genuinely nonlinear one-dimensional systems (the Keyfitz-Kranzer system, the isentropic generalized Chaplygin gas dynamics equations, and the isentropic gas dynamics equations for polytropic gases with vanishing pressure). Besides approximating solutions that contain shocks and rarefaction waves, the focus is on approximating solutions which contain singular and delta shocks.
Numerical Study of Singular and Delta Shock Solutions Using a Large Time Step Method,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 13,
2, Article 30.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss2/30