In the present paper, three complicated non- linear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method ...In the present paper, three complicated non- linear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method （AGM）. Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method （Runge-Kutte 4th）. Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.展开更多
In this paper, we aim to promote the capability of solving two complicated nonlinear differential equa- tions： 1） Static analysis of the structure with variable cross section areas and materials with slope-deflectio...In this paper, we aim to promote the capability of solving two complicated nonlinear differential equa- tions： 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.展开更多
文摘In the present paper, three complicated non- linear differential equations in the field of vibration, which are Vanderpol, Rayleigh and Duffing equations, have been analyzed and solved completely by Algebraic Method （AGM）. Investigating this kind of equations is a very hard task to do and the obtained solution is not accurate and reliable. This issue will be emerged after comparing the achieved solutions by numerical method （Runge-Kutte 4th）. Based on the comparisons which have been made between the gained solutions by AGM and numerical method, it is possible to indicate that AGM can be successfully applied for various differential equations particularly for difficult ones. The results reveal that this method is not only very effective and simple, but also reliable, and can be applied for other complicated nonlinear problems.
文摘In this paper, we aim to promote the capability of solving two complicated nonlinear differential equa- tions： 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.
