Large time step generalizations of Glimm's scheme for systems of conservation laws
Two generalizations of Glimm's scheme for Courant numbers larger than 0.5 are discussed. For the first generalization it is shown that for any fixed Courant number if a sequence of approximate solutions converges to a limit u, then u is a weak solution. It is proven that the family of approximate solutions contains a convergent subsequence. For the second generalization it is shown that the family of approximate solutions for a system of isothermal gas dynamics equations contains a convergent subsequence provided that the total variation of the initial data is bounded.
system of isothermal gas dynamics equations
scientific article; zbMATH DE number 4178682