Innovation in Engineering Field and Basic Sciences in the Analytical Solution of Nonlinear Partial Differential Equations (PDE) by new Approaches AYM

In this paper, for the first time, we exposure analytical methods for solving complicated nonlinear differential equations in engineering fields and basic sciences, where these new methods can easily and flexibly analyze complex engineering problems. Some complicated highly nonlinear differential equations (including ODEs and PDEs) in different fields. In this article, we present an innovative method called Akbari-Yasna Method(AYM). In this article, we want to solve equations like the following in the fields of engineering and basic sciences:

This virgin method can be successfully applied in various engineering fields such as petroleum industry (solid, fluid, mass and heat transfer, dynamic, quantum physic, chemical reactors, electronics, applied sciences, economics, and etc.). Besides, the methodology behind these techniques is completely understandable, easy to use, and users with common knowledge of mathematics will be capable of solving the most complicated equations at low calculation cost.

Keywords: New Approach; Akbari-Yasna-Method (AYM); Nonlinear Partial Differential Equation (PDE); Innovation in Engineering Mathematics Fields