Backward Iterations for Solving Integral Equations with Polynomial Nonlinearity

The theory of adjoint operators is widely used in solving applied multidimensional problems with the Monte Carlo method. Efficient algorithms are constructed using duality principle for many described linear integral equations second kind. On other hand, important applications designing experiments were suggested by G.I. Marchuk and his colleagues their respective works. Some results obtained these fields also generalized to case nonlinear operators. Linearization methods mostly that purpose. Lyapunov–Schmidt polynomial methods. However, interesting questions this subject area remain open. New about dual processes method presented. In particular, Markov process branching corresponding unbiased estimate functional solution equation general form. possibility constructing an operator a one discussed.