Detecting Roots of Nonlinear Equations through a Novel Differential Evolution Algorithm

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 re-initialize, 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.