In this paper, we consider the nonlinear Volterra-Fredholm-Hammerstein integral equations. The approximate solution for the nonlinear Volterra-Fredholm-Hammerstein integral equations is obtained by using the Tau-Collocation method. To do this, the nonlinear Volterra-Fredholm-Hammerstein integral equations is transformed into a system of nonlinear algebraic equations in matrix form. Thus by solving this system unknown coefficients are obtained. The spectral rate of convergence for the proposed method is established in the L 2 -norm. The numerical results obtained with minimum amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the Tau-collocation method is of high accuracy, more convenient and efficient for solving nonlinear Volterra-Fredholm-Hammerstein integral equations.
['Zienab Gouyandeh', 'Tofigh Allahviranloo', 'Atefeh Armand']
Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via Tau-collocation method with convergence analysis