algebraic nonlinearity in volterra-hammerstein equations

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we also generalize this upper bound for nonlinear volterra integro-differential and volterra- hammerstein integral equations of mixed type . finally, several numerical examples are gken to show effectiveness of these bounds