singular integro-differential equation, finite element approxima-tion, convergence, error analysis, Applied mathematics. Quantitative methods, T57-57.97

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.