A real analytical integral formula for a simple root of a system of two nonlinear equations
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Date
1986
Authors
Ioakimidis, Nikolaos
Journal Title
Journal ISSN
Volume Title
Publisher
University of Niš
Abstract
A 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.