TY  - JOUR
T1  - Neural network, differential equation, PSO algorithm, sensitivity, adjustable, convergnece
AU - Behzadi, Saadat AU - Miri, Maliheh 
JO  - Journal of Engineering and Applied Sciences
VL  - 14
IS  - 23
SP  - 8576
EP  - 8584
PY  - 2019
DA  - 2001/08/19
SN  - 1816-949x
DO  - jeasci.2019.8576.8584
UR  - https://makhillpublications.co/view-article.php?doi=jeasci.2019.8576.8584
KW  - Neural network
KW  -differential equation
KW  -PSO algorithm
KW  -sensitivity
KW  -adjustable
KW  -convergnece
AB  - 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.
ER  -