Akram Javadi - Department of Mathematics, Ardabil branch, Islamic Azad University, Ardabil, Iran
Nasser Mikaeilvand - Department of Mathematics, Ardabil branch, Islamic Azad University, Ardabil, Iran
Hassan Hosseinzdeh - Department of Mathematics, Ardabil branch, Islamic Azad University, Ardabil, Iran

The analytical methods are not able to solve some of the differential equations. For this reason, the approximate methods like intelligent algorithms are used to reach an answer with the error as low as possible. In this article, a new method has been presented to solve ordinary and partial differential equations (PDEs) which is based on a hierarchical method and the group search optimizer (GSO)-based graph theory. GSO algorithm is an optimization method inspired from the searching behavior of animals and has been implemented based on the producer-scrounger model. It should be noted that according to the aforementioned pattern, the scan mechanisms of animals are symbolically considered here to solve optimization problems. This algorithm has the ability to expand the search space of the genetic algorithm (GA) due to the presence of ranger operator and on the other hand, it has a high convergence speed to find the best answers due to use scrounger model. Therefore, in this article, the best possible answer for PDEs is provided from all possible answers with the least error.

Partial differential equations (PDE), GSO algorithm, Dependent error minimization, Graph theory