The essence of Glimm’s scheme. (English) Zbl 0882.35009

Schochet, Steven

Ding, Xiaxi (ed.) et al., Nonlinear evolutionary partial differential equations. Proceedings of the international conference, Beijing, China, June 21–25, 1993. Providence, RI: American Mathematical Society. AMS/IP Stud. Adv. Math. 3, 355-362 (1997).

A variant of the Glimm’s scheme is suggested which combines the esthetic features of both the original scheme and front-tracking one by Bressan. The modification of the Bressan’s scheme allows to avoid the use of nonphysical waves. The properties of convergence and consistency are proven for the introduced scheme.
For the entire collection see [Zbl 0869.00036].

Reviewer: S.V.Utyuzhnikov (Moskva)

MSC:

35A35	Theoretical approximation in context of PDEs
35L65	Hyperbolic conservation laws

Keywords:

convergence and consistency; weak solutions; front tracking