Numerical solution and its analysis for a system of hypersingular integral equations

A system of hypersingular integral equations occurs quite naturally in several branches of science and engineering during the formulation of many boundary value problems. The analytical solution is known for the system of dominant equations. However, there are many real world problems such as crack problems occur in the field of fracture mechanics which may not be formulated as system of dominant equations. Therefore, we propose a numerical method to find the approximate solution for such generalized form. The convergence of the proposed method is proved in LN2 space. This convergence helps to derive theoretical error bound for the error between the exact and the approximate solution. An application of the proposed method in finding numerical solution of hypersingular integral equation over the curves is shown. Finally, the derived theoretical error bound is numerically calculated and validated with the help of numerical examples.