Improved polynomial approximations for the solution of nonlinear integral equations

In this paper, the solutions of nonlinear integral equations, including volterra, fredholm,volterrafredholm of first and second kinds, are approximated as a linear combination of some basicfunctions. the unknown parameters of an approximate solution are obtained based on minimizationof the residual function. in addition, the existence and convergence of these approximate solutions areinvestigated. in order to use newton's method for minimization of the residual function, a suitable initialpoint will be introduced. moreover, to confirm the efficiency and accuracy of the proposed method, somenumerical examples are presented. it is shown that there are considerable improvements in our resultscompared with the results of the existing methods. all numerical computations have been performed ona personal computer using maple 12.