Ioakimidis, Nikolaos2023-11-042023-11-041986http://elibrary.matf.bg.ac.rs/bitstream/handle/123456789/2509/FU%20FR.pdf?sequence=1#page=62https://hdl.handle.net/10889/26150A method for the closed-form solution of two real nonlinear algebraic or transcendental equations, f(x,y) = 0, g(x,y) = 0, possessing one simple root (x0, y0) in a finite domain of the Oxy-plane is proposed. This method is based on the Picard method for the calculation of the number of roots of a system of nonlinear equations or, more explicitly, on the classical Gauss (or divergence) theorem in elementary mathematical analysis. The resulting formulae for x0 and y0 contain integrals including the functions f and g and their first partial derivatives. The present results generalize earlier relevant results for a single nonlinear equation.en