Solving ordinary differential equations using an optimization technique based on training improved artificial neural networks.

The solution of ordinary differential equations (ODEs) arises in a wide variety of engineering problems. This paper presents a novel method for the numerical solution of ODEs using improved artificial neural networks (IANNs). In the first step, we derive an approximate solution of ODEs by artificial neural networks (ANNs). Then, we construct a joint cost function of network system, it consists of several error functions corresponding to different sample points, and we reformulate Levenberg–Marquardt (RLM) algorithm to adjust the network parameters. The advantages of this method are high calculation accuracy and fast convergence speed compared with other existed methods, also increasing the simulation stability of ANNs method. The performance of the new proposed method in terms of calculation accuracy and convergence speed is analyzed for several different types of nonlinear ODEs. [ABSTRACT FROM AUTHOR]