Numerical Treatment of Hypersingular Integral Equations with Application to Crack Mechanics
Iovane, G. ; Sumbatyan, M. A.
arXiv, 0307025 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-07-10
Classification:  Mathematical Physics,  Mathematics - Numerical Analysis 
@article{0307025,
     author = {Iovane, G. and Sumbatyan, M. A.},
     title = {Numerical Treatment of Hypersingular Integral Equations with Application
  to Crack Mechanics},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0307025}
}

Iovane, G.; Sumbatyan, M. A. Numerical Treatment of Hypersingular Integral Equations with Application
  to Crack Mechanics. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0307025/