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

摘要

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.