Authors : Saadat Behzadi and Maliheh Miri
Abstract: In this study, a novel hybrid method is presented for the solution of Ordinary Differential Equations (ODEs) with neural network that is trained by using PSO algorithm. Although, many studies for solving ODEs are available now, this method has more advantages such as fast convergence and also little error. A solution of ODE is written as a sum of two parts. The first part involve no adjustable parameters that satisfies the initial condition and the second part contains a feed forward neural network containing adjustable parameters which use the PSO algorithm. Therefore, by using both parts satisfied the initial condition and also the neural network is train to solve ODEs. The proposed method is applicable to solve ordinary differential equations and systems of Ordinary Differential Equations (SODEs). Finally, there are several examples to analysis sensitivity of the convergence.
Saadat Behzadi and Maliheh Miri, 2019. Neural network, differential equation, PSO algorithm, sensitivity, adjustable, convergnece. Journal of Engineering and Applied Sciences, 14: 8576-8584.