ABSTRACT
This chapter deals with discontinuous solutions and methods of their computation. Prior to constructing the algorithms for computing discontinuous solutions of integral conservation laws, one will need to generalize the concept of solution to a differential initial (boundary) value problem. The objective is to make it meaningful and equivalent to the original integral conservation law even in the case of discontinuous solutions. This chapter makes use of a simple example to illustrate the transition from the problem formulated in terms of an integral conservation law to an equivalent differential problem. In the method of characteristics, the chapter uses special formulae to describe the evolution of discontinuities that appear in the process of computation, i.e., as the time elapses.
