Swarm Intelligence for the Solution of Problems in Differential Equations

In this article, swarm intelligence approach is proposed for the solution of problems involved in differential equations of first order. The modeling of these problems is performed by artificial neural network that have universal approximation capabilities. A new particle swarm optimization algorithm is used to optimize the adaptive weights of neural network. The proposed method is successfully applied to a number of test problems and comparison is made with analytical, standard numerical methods and evolutionary computational technique like genetic algorithm. The solution is achieved on the continuous grid of time instead of discrete unlike other numerical techniques. It is found that this stochastic method can provide accurate results from some of classical numerical approaches and is comparative to recent evolutionary technique like genetic algorithm. The solution is found with a uniform accuracy of MSE 10^-09.