Particle swarm optimization algorithm for solving singular nonlinear equations

Singular nonlinear equations is a class of important and difficult problem.Based on particle swarm optimization algorithm,a method for solving singular nonlinear equations is proposed in this paper.The equations are transformed into optimization problem without constraints,to be solved by particle swarm optimization algorithm.This algorithm,free from the limitation of the form of the equations,avoids such complicated processes as calculating derivative and finding inverse of a matrix,and gives an exact numerical solution.Simulation results show that the algorithm is feasible and effective.This algorithm not only provides a new algorithm for solving singular nonlinear equations, but also enlarges the application area of the particle swarm optimization algorithm.