A Particle Swarm Runge-Kutta Optimization Algorithm for Solving the BVP of Ordinary Differential Equation

摘要

We transform the boundary value problem of ordinary differential equation into an unconstrained optimization problem. To find an effective algorithm for that problem, we incorporate the Runge-Kutta (R-K) method into the Particle Swarm Optimization algorithm (PSO) and construct a new PSO based R-K method. We use several famous boundary value problem to testify the efficiency of the proposed algorithm. The computational results show that the proposed new method is quite promising.