| Abstract: | A parabolic method consisting of replacement of the stream acceleration ?xx in the non-linear member of (1.1) by a specially chosen constant has been proposed [1] for the solution of the mixed-type transonic equation with boundary conditions on the profile, and the solution of the linear parabolic-type equation obtained can be considered as a certain approximation to the solution of the initial problem. An improvement of the parabolic method is the method of local linearization [2] (see [3] also), in which the acceleration ?xx fixed from the beginning is replaced by a function of the coordinate x which satisfies some condition. An ordinary first-order differential equation is obtained for the velocity distribution along the profile in [2]. Another method of “defrosting” the acceleration ?xx “frozen” from the beginning is proposed in this paper; a second-order ordinary differential equation is obtained for the velocity on the profile, which permits getting rid of some disadvantages of the local linearization method. Several solutions of (2.3) are presented in comparison to known exact solutions. |
