A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem

The nonlinear integral equations arise in the theory of parabolic boundary value problems, engineering, various mathematical physics, and theory of elasticity 1–3 . In recent years, several analytical and numerical methods of this kind of problems have been presented 4, 5 . Analytically, the decomposition methods are used in 6, 7 . The classical method of successive approximations was introduced in 8 , while some kind of appropriate projection such as Galerkin and collocation methods have been applied in 9–13 . These methods often transform integral or integrodifferential equations into a system of linear algebraic equations which can be solved by direct or iterative methods. In 14 , the authors used Taylor series to solve the following nonlinear Volterra-Fredholm integral equation: