A new numerical method for approximation of hypersingular integrals

Abstract

In this paper, we investigate the construction of a new numerical method for approximating Cauchy and Hilbert hypersingular integrals, which are important in various fields such as engineering, physics, and applied mathematics due to their significant role in the solution of singular and hypersingular integral equations. To validate the theoretical analysis, we have conducted several numerical examples implemented in the MATLAB programming language. The obtained results demonstrate the stability, accuracy, and efficiency of the suggested approach. The proposed quadrature formulas are not only straightforward to compute but also scalable, ensuring the reliability and applicability of the method to a wide range of practical problems. This makes the method particularly useful for real-world applications requiring high computational efficiency.