Significant progress in solution of nonlinear equations at displacement of structure and heat transfer extended surface by new AGM approach

In this paper, we aim to promote the capability of solving two complicated nonlinear differential equations: 1) Static analysis of the structure with variable cross section areas and materials with slope-deflection method; 2) the problem of one dimensional heat transfer with a logarithmic various surface A(x) and a logarithmic various heat generation G(x) with a simple and innovative approach entitled “Akbari-Ganji’s method” (AGM). Comparisons are made between AGM and numerical method, the results of which reveal that this method is very effective and simple and can be applied for other nonlinear problems. It is significant that there are some valuable advantages in this method and also most of the differential equations sets can be answered in this manner while in other methods there is no guarantee to obtain the good results up to now. Brief excellences of this method compared to other approaches are as follows: 1) Differential equations can be solved directly by this method; 2) without any dimensionless procedure, equation(s) can be solved; 3) it is not necessary to convert variables into new ones. According to the aforementioned assertions which are proved in this case study, the process of solving nonlinear equation(s) is very easy and convenient in comparison to other methods.