The convergence of a completely conservative difference scheme for gas- dynamic equations in Euler variables (Q1802585)

Initial-value problem for one-dimensional Euler equations with a source term is considered. The second-order completely conservative scheme is introduced. The following results are presented: (1) the proof of the existence and uniqueness of its solution; (2) the energetic inequality for the estimate for the error of the method; (3) the proof of the second-order convergence in \(L_ 2\) norm of the difference solution to the exact one. The rate of convergence is illustrated by a numerical example.