Hydrothermal analysis of MHD nanofluid (TiO2-GO) flow between two radiative stretchable rotating disks using AGM

Hydrothermal analysis of MHD squeezing mixture fluid suspended by hybrid nanoparticles between two parallel plates

Hydrothermal analysis of magneto hydrodynamic nanofluid flow between two parallel by AGM

In this study, stochastic numerical treatment is presented for boundary value problems (BVPs) arising in nanofluidics for nonlinear Jeffery–Hamel flow (NJ-HF) equations using feed-forward artificia...

Design of bio-inspired computing technique for nanofluidics based on nonlinear Jeffery–Hamel flow equations

Hermite polynomial-based functional link artificial neural network FLANN is proposed here to solve the Van der Pol-Duffing oscillator equation. A single-layer hermite neural network HeNN model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed error function. The Van der Pol-Duffing and Duffing oscillator equations may not be solved exactly. Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. Three mathematical example problems and two real-life application problems of Van der Pol-Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method. HeNN approximate solutions have been compared with results obtained by the well known Runge-Kutta method. Computed results are depicted in term of graphs. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Thus, the proposed HeNN method is efficient. The results reveal that this method is reliable and can be applied to other nonlinear problems too.

Hermite functional link neural network for solving the van der pol-duffing oscillator equation

In the present paper, three complicated nonlinear 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.

Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

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.

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

In this study, the effects of magnetic field and nanoparticle on the Jeffery-Hamel flow are studied using two powerful analytical methods, Homotopy Perturbation Method (HPM) and a simple and innovative approach which we have named it Akbari-Ganji’s Method(AGM). Comparisons have been made between HPM, AGM and Numerical Method and the acquired results show that these methods have high accuracy for different values of α, Hartmann numbers, and Reynolds numbers. The flow field inside the divergent channel is studied for various values of Hartmann number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.

Investigating Jeffery-Hamel flow with high magnetic field and nanoparticle by HPM and AGM

Investigation on non-linear vibration in arched beam for bridges construction via AGM method

In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (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 simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

M. R. Akbari

Papers

Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM

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

Investigating Jeffery-Hamel flow with high magnetic field and nanoparticle by HPM and AGM

Investigation on non-linear vibration in arched beam for bridges construction via AGM method

Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method