Investigation of a new method for the numerical solution of a system of hypersingular integral equations

The system of hypersingular integral equations occurs naturally in several branches of scienceand engineering during the formulation of many boundary value problems. The analytical solution for thesystem of dominant equations is known. However, many real-world problems, such as cracking problemsin fracture mechanics, may not be formulated as a set of dominant equations. Therefore, we propose anumerical method to find an approximate solution for such a generalized form. The convergence of theproposed method is proved. This convergence helps to derive the error bound for the error between theexact and the approximate solution. Finally, by providing a numerical example, the efficiency of thismethod will be presented.