A direct numerical method for solving the Föppl-Hencky equation

We rewrite the Foppl-Hencky equation as an unconstrained optimization, and then solve the equation by an optimization algorithm. The optimization algorithm is constructed by combining the intelligent algorithms with an numerical algorithm for different equation. We give three numerical experiments, and the simulation results show that the Rounge-Kutta method based particle swarm optimization algorithm solves the equation very well.