Tau approximation method for the weakly singular Volterra-Hammerstein integral equations

In this paper, we propose a useful method based on the Tau method with arbitrary bases to find the numerical solution of weakly singular Voletrra-Hammerstein integral equations. In this scheme an operational approach using the orthogonal polynomial bases is presented for converting the problem under consideration to its matrix-vector representation. Error analysis of this method is also presented. Some numerical examples are provided to illustrate the accuracy and computational efficiency of the method.