solving mixed singular integro-differential equation (ide) using the finite elements method

In this work, we describe a new method for the calculation of the numerical solution of the mixed singular integro-differential equation. the method is mainly based on a finite element approximation. for this purpose, we obtain the variational form of the problem under consideration. the result-ing system has been approximated numerically by linear b-spline function. the method of convergence and its order of convergence are established. finally, to investigate the accuracy of the proposed method some test ex-amples are presented. the numerically obtained results are compared with another method for the validity of our results and shown by some tables and figures.