result in non-potential flow, violating the initial assumptions. Characteristics may fail to cover part of the domain of the PDE. This is called a rarefaction, and indicates the solution typically exists only in a weak, i.e. integral equation, sense. The direction of the characteristic lines indicates the flow of values through the solution, as the example above demonstrates. This kind of knowledge is useful when solving PDEs numerically as it can indicate which finite difference scheme is best for the problem. See also Method of quantum characteristics Notes References . External links Prof. Scott Sarra tutorial on Method of Characteristics Prof. Alan Hood tutorial on Method of Characteristics Partial differential equations Hyperbolic partial differential equations