Keyword: «boundary catastrophe»

Methods for calculating the special function of the wave catastrophe B3 and its first derivative describing the A2 type focusing with an edge are investigated. The caustic and radial structures of this feature are constructed. The characteristic amplitude-phase cross sections of the special function and its derivative are calculated. The method of turning the integration contour and the method of ordinary differential equations in both accuracy and speed are considered and compared. It is shown that the method of ordinary differential equations works stably both in the region of negative values of the first two parameters of the special function and in the region of positive values, and the method of turning the integration contour only in the region of positive values. The calculation time of a special function by the method of ordinary differential equations is an order of magnitude less than the calculation time by the method of turning the integration contour.