The Particle Swarm Shooting Method for Solving the Bratu's Problem.

We transform the Bratu's problem directly into an unconstrained optimization problem, and then solve it by a simple algorithm, which combining the particle swarm optimization algorithm with Runge-kutta method together. We compare the numerical performance of the proposed optimization algorithm with the existing methods, and the numerical results show that the proposed new method is quite promising. [ABSTRACT FROM AUTHOR]