Exact Solutions of the Space Charge Equation Using the Hodograph Method

In this paper we show that a hodograph method first introducedby Budd & Wheeler (1987) to develop a new numerical algorithmto solve the space charge equation •()=0 can be employedto derive all the known exact solutions, which have recentlybeen found by Smith (1988). All these solutions are shown tobe separable solutions of the equations resulting from the applicationof the hodograph transformation. We also briefly describe thisnew numerical method and use one of the exact solutions to demonstrateits accuracy.