A real closed-form integral formula for roots of nonlinear equations
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Ioakimidis, Nikolaos
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Abstract
An analytical integral formula for a single simple root of a nonlinear equation in a finite interval is proposed. The derivation of this formula is based on Picard's method for the number of roots of nonlinear equations and on Green's theorem. The present formula is particularly useful for the location of roots of nonanalytic functions. A comparison between the present formula and a related classical formula based on the theory of analytic functions is also made.
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Keywords
Simple roots, Simple zeros, Nonlinear equations, Algebraic equations, Transcendental equations, Nonanalytic functions, Analytic functions, Picard's method, Closed-form formulae, Analytical formulae, Integral formulae, Green's theorem