Mathematical Modeling of the Wave-Field Structure in the Vicinity of Edge Catastrophe B4

Methods for calculating the special function of wave catastrophe B 4 and its first derivatives, which describe edge focusing of the caustic-tip type with an edge, are studied. The caustic and ray structures of this singularity are constructed. The characteristic amplitude–phase sections of the speci...

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Bibliographic Details
Published in:Journal of communications technology & electronics 2023-12, Vol.68 (Suppl 3), p.S338-S348
Main Authors: Domnina, M. S., Kryukovsky, A. S., Rastyagaev, D. V.
Format: Article
Language:English
Subjects:
Communications Engineering
Contours
Derivatives
Differential equations
Engineering
Mathematical Modeling of Physical Processes
Networks
Ordinary differential equations
Rotation
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Summary:Methods for calculating the special function of wave catastrophe B 4 and its first derivatives, which describe edge focusing of the caustic-tip type with an edge, are studied. The caustic and ray structures of this singularity are constructed. The characteristic amplitude–phase sections of the special function and its derivatives are calculated. The method of rotation of the integration contour and the method of ordinary differential equations are considered and compared both in terms of accuracy and speed. It is shown that the method of ordinary differential equations works stably in the region of negative values of the first two parameters of the special function, and the method of rotation of the integration contour exhibits stability in the region of positive values. Thus, the approaches are complementary. However, the calculation time for the method of ordinary differential equations is an order of magnitude less than the time for the method of rotation of the integration contour.
ISSN:1064-2269
1555-6557
DOI:10.1134/S1064226923150056