an efficient collocation method for the numerical solutions of the pantograph-type volterra hammerstein integral equations and its convergence analysis

In this work, we consider a collocation method for solving the pantograph-type volterra hammerstein integral equations based on the first kind chebyshev polynomials. we use the lagrange interpolating polynomial to approximate the solution. the convergence of the presented method has been analyzed by over estimating for error. finally, some illustrative examples are given to test the accuracy of the method. the presented method is compared with the legendre tau method.