A dynamical system method for solving nonlinear ill-posed problems (Q2479204)

Nonlinear ill-posed operator equations of the type \(F(t,u(t))=z(t)\), where \(F\) is a Fréchet differentiable operator acting between two Hilbert spaces may be solved approximately by the dynamical system method that regularizes the problem. Employing Lyapunov's theory, the authors study stability of the approximate solutions as well as convergence. Finally, a numerical example is given for an integral operator of Hammerstein type.