Detecting Roots of Nonlinear Equations through a Novel Differential Evolution Algorithm

摘要

Though many numerical methods have been put for nonlinear equations, their convergence and performance are highly sensitive to the initial guesses of the solution pre-supplied.However, the selection of good initial guess is often of hard work.Aiming at this, a novel approach is proposed to resolve nonlinear equations. It takes genetic algorithms' new achievement differential evolution algorithms as the main technique. With a function deflection technique and a novel space contraction method to reinitialize,it resolve nonlinear equations by transform them into correspondent optimization problems. Convergence reliability, computational cost and applicability of different algorithms were compared by testing several classical nonlinear equations and a benchmark mechanics problem. The numerical experiments done show that the put approach has reliable convergence probability,high convergence rate and solution precision. And DE is a successful approach in solving equations both in theory and application.