The Tricomi Problem

In this chapter we use the method of difference potentials for computing solutions of some difference analogs of the Tricomi problem. The classical Tricomi problem is a typical example of numerous problems arising in the study of plane transonic flows of compressible gas, e.g., of flows in the Laval nozzle or flows around contours. The Tricomi equation has the form (I)$$ y\frac{{\partial ^2 u}} {{\partial x^2 }} + \frac{{\partial ^2 u}} {{\partial y}} = 0. $$ It is an equation of mixed type, since it is elliptic for y > 0 and hyperbolic for y < 0.