2003/07/10 by Gerardo Iovane, Iovane, G., M.A. Sumbatyan +1
Engineering · Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.math-ph/0307025
openalex publication_date 2003/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we present a treatment of hypersingular integrals and integral equations. It is shown the equivalence of different definitions of hypersingular integrals. Then we construct explicit analytical solution to a characteristic equation and prove convergence of the collocation method to this solution. Further, we expand these results to full hypersingular kernels, and give a demonstration of the developed method to some problems of crack mechanics including crack problem for porous elastic materials, in the framework of Cowin-Nunziato model.