Error of the a-method for solving Volterra integral equations with polynomial nonlinearities

Abstract

We mention that the fundamental merit of the a-method, attracting the growing attention of specialists, are, first of all, the high accuracy of the order of the best (and in a series of cases, asymptotically best) approximation of the desired functions by algebraic polynomials and the resulting non-saturation of the a-method. This explains also the big advantage of the a-method over the finite difference methods for solving differential equations [ii].