Numerical computation of diffraction catastrophes with codimension eight

Area of Science:

• Computational physics
• Optical physics
• Applied mathematics

Background:

• Diffraction catastrophes are complex wave phenomena crucial in optics.
• Evaluating specific families like X(9) presents significant computational challenges.
• Existing methods may lack efficiency or broad applicability.

Purpose of the Study:

• To present a novel computational strategy for evaluating X(9) family diffraction catastrophes.
• To utilize power series expansions and the Weniger transformation for this evaluation.
• To assess the effectiveness and implementation ease of the proposed approach.

Main Methods:

• Development of power series expansions for the (0)X(9) subfamily.
• Application of the Weniger transformation algorithm to accelerate series convergence.
• Conducting numerical experiments to validate the strategy.

Main Results:

• The proposed power series expansions provide meaningful representations of the (0)X(9) subfamily.
• The Weniger transformation significantly enhances the convergence of these series.
• Numerical experiments confirm the effectiveness and practical utility of the computational strategy.

Conclusions:

• The presented computational strategy offers an effective means for evaluating X(9) diffraction catastrophes.
• The combination of power series and the Weniger transformation is a powerful tool in this domain.
• This approach facilitates the study of complex optical phenomena.