Solution of a non-trivial space charge problem by the hodographic method

A numerical technique for solving the discontinuous injection space-charge problem is described. This technique is based upon the hodographic method studied by Budd and Wheeler. In order to avoid the difficulties introduced by the vanishing charge density the domain is split into two subdomains with an unknown common boundary. Each of these subproblems is then solved by the hodographic method, and an extra boundary condition is used to update the position of the unknown boundary.