On the numerical evaluation of cuspoid diffraction catastrophes
1Dipartimento di Elettronica Applicata and CNISM, Università degli Studi Roma Tre, Rome, Italy. borghi@uniroma3.it
Summary
A new computational method simplifies evaluating cuspoid diffraction catastrophes, essential for describing wave fields near caustics. This approach proves effective and easy to implement for complex and real arguments.
Area of Science:
- Physics
- Computational Mathematics
- Wave Optics
Background:
- Cuspoid diffraction catastrophes are crucial for modeling wave fields near stable caustics.
- Accurate evaluation of these functions is vital in various scientific and engineering applications.
Purpose of the Study:
- To propose a simple and effective computational approach for evaluating cuspoid diffraction catastrophes.
- To numerically investigate the Weniger transformation's action on Pearcey and swallowtail functions.
Main Methods:
- Representing Pearcey and swallowtail functions using convergent series expansions.
- Numerically applying the Weniger transformation to these series for real and complex arguments.
- Conducting numerical experiments to validate the method's effectiveness and ease of implementation.
Main Results:
- Demonstrated the effectiveness of the proposed computational method for cuspoid diffraction catastrophes.
- Provided quantitative comparisons with previously published results, showing good agreement.
- Confirmed the implementative ease of the numerical approach.
Conclusions:
- The proposed computational method offers a straightforward and efficient way to evaluate cuspoid diffraction catastrophes.
- This technique is valuable for analyzing wave fields and related phenomena in optics and physics.
- The numerical study validates the method's accuracy and practical utility.
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