@article{MAKHILLJEAS2019142318711,
    title = {Neural network, differential equation, PSO algorithm, sensitivity, adjustable, convergnece},
    journal = {Journal of Engineering and Applied Sciences},
    volume = {14},
    number = {23},
    pages = {8576-8584},
    year = {2019},
    issn = {1816-949x},
    doi = {jeasci.2019.8576.8584},
    url = {https://makhillpublications.co/view-article.php?issn=1816-949x&doi=jeasci.2019.8576.8584},
    author = {Saadat and},
    keywords = {Neural network,differential equation,PSO algorithm,sensitivity,adjustable,convergnece},
    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.}
    }