{"title":"Mathematical Modeling of the Wave-Field Structure in the Vicinity of Edge Catastrophe B4","authors":"M. S. Domnina, A. S. Kryukovsky, D. V. Rastyagaev","doi":"10.1134/s1064226923150056","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Methods for calculating the special function of wave catastrophe B<sub>4</sub> 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.</p>","PeriodicalId":50229,"journal":{"name":"Journal of Communications Technology and Electronics","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Communications Technology and Electronics","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1134/s1064226923150056","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
引用次数: 0
Abstract
Methods for calculating the special function of wave catastrophe B4 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.
期刊介绍：
Journal of Communications Technology and Electronics is a journal that publishes articles on a broad spectrum of theoretical, fundamental, and applied issues of radio engineering, communication, and electron physics. It publishes original articles from the leading scientific and research centers. The journal covers all essential branches of electromagnetics, wave propagation theory, signal processing, transmission lines, telecommunications, physics of semiconductors, and physical processes in electron devices, as well as applications in biology, medicine, microelectronics, nanoelectronics, electron and ion emission, etc.
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