Nonlinear Fundamental Differential Equations of Langmuir Blodgett and Boguslavski and Its Analytical Solution with AGM Approach

Hassanvand N, Fayazi F, Adineh A, Rokni S, Sadeghifar T, Sarkardeh Z, Shafiei GA, Kasmaei Najaf Abadi H and Ghazagh N

Published on: 2023-11-25


In this paper, we investigate and analytically solve two fundamental and very complicated non-linear differential equations in engineering and basic sciences, which are called Langmuir Blodgett and Langmuir Boguslavski equations. In this article, we present these two nonlinear differential equations analytically using a simple and innovative method, which we have named the Akbari-Ganji Method, or AGM.

Comparisons have been made between AGM and Numerical Solution and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The reasons of selecting AGM for solving  differential equations in the all fields engineering and basic science, such as fluid, Vibrations, Strength of materials, Chemical engineering, physics etc. in comparison with the other manners are as follows: The solution procedure will be very easy by assuming a finite series of polynomials with constant coefficients as the answer of the equation and also in this method the user is able to remove the dilemma of boundary conditions shortage which has been explained in the foregoing part of this case study . According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison with the other methods.