Analytical Numerical Method for Solving Integral Hammerstein Equations Arising in Free Phase Problems

The nonlinear integral equations of Hammerstein type arise in problems with a free phase. A polynomial approach is used to solve such equations. A system of transcendental equations is constructed to find complex parameters (polynomial roots). For more general optimization problems, this system is supplemented by a linear integral equation. For the case of solutions vanishing on the finite interval, a system of integralfunctional equations is obtained. The branching of solutions is investigated.