A NEW DYNAMICAL SYSTEMS METHOD FOR NONLINEAR OPERATOR EQUATIONS

A new dynamical systems method is studied for solving nonlinear operator equation . This method consists of the construction of a nonlinear dynamical systems, that is, a Cauchy problem , where Φ is a suitable operator, which has the following properties: i) :∃u(t) ∀t > 0, ii) :∃u(∞), and iii) . Conditions on are given which allow one to chosen Φ such that i), ii), and iii) hold. This method yields also a convergent iterative method for finding true solution y. Stable approximation to a solution of the equation is constructed by this DSM when f is unknown but fδ is known, when ||f − fδ|| ≤ δ.