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Constructing analytic solutions on the Tricomi equation

Emran Khoshrouye Ghiasi, Reza Saleh
2018 Open Physics  
In this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to
more » ... e well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.
doi:10.1515/phys-2018-0022 fatcat:7gly33l37vgldpgdfb4565y5qu

A Mathematical Approach Based on the Homotopy Analysis Method: Application to Solve the Nonlinear Harry-Dym (HD) Equation

Emran Khoshrouye Ghiasi, Reza Saleh
2017 Applied Mathematics  
Khoshrouye Ghiasi, R. Saleh DOI: 10.4236/am.2017.811113  ...  Khoshrouye Ghiasi, R. Saleh DOI: 10.4236/am.2017.811113 1553 Applied Mathematics E. Khoshrouye Ghiasi, R. Saleh DOI: 10.4236/am.2017.811113 1556 Applied Mathematics through the HAM.  ... 
doi:10.4236/am.2017.811113 fatcat:hiq6qbvb7jg53lg27rvlbzal2i

Modeling and Analysis of Electrostatically Actuated MEMS under Combined Nonlinearities, Lorentz Force, and Mechanical Shock

Emran Khoshrouye Ghiasi
2016 J of Control Science and Engineering  
This paper shows an analysis of M EM S (micro electro mechanical systems) due to Lorentz force and mechanical shock. The formulation is based on a modified couple stress theory, the von Kármán geometric nonlinearity and Reynolds equation as well. The model contains a silicon microbeam, which is encircled by a stationary plate. The non-dimensional governing equations and associated boundary conditions are then solved iteratively through the Galerkin weighted method. The results show that pull-in
more » ... voltage is dependent on the geometry nonlinearity. It is also demonstrated that by increasing voltage between the silicon microbeam and stationary plate, the pull-in instability happens.
doi:10.17265/2328-2231/2016.02.004 fatcat:6umod5w3mvhtzadx4fv2utgn2u

2D FLOW OF CASSON FLUID WITH NON-UNIFORM HEAT SOURCE/SINK AND JOULE HEATING

Emran Khoshrouye Ghiasi, Reza Saleh
2018 Frontiers in Heat and Mass Transfer  
This fact is also illustrated in Aziz (2016) and Khoshrouye Ghiasi and Saleh (2019).  ...  It should be noted that the Casson fluid is affected by the viscous force while the Lorentz force tends to decelerate flow of the fluid and retards its motion (Khoshrouye Ghiasi and Saleh, 2018c).  ... 
doi:10.5098/hmt.12.4 fatcat:smevv5cdjjefta6gbabl4gu32q

HBA analysis of generalized viscoelastic fluids

Emran Khoshrouye Ghiasi, Department of Mechanical Engineering, College of Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran, Reza Saleh, Department of Mechanical Engineering, College of Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2019 Engineering and Applied Science Letters  
Generating homotopy-based approaches (HBAs) in thermal-fluid sciences is an efficient manner for finding absolutely convergent series expansions. The main objective of this paper is to analyze the viscoelastic Walter's B fluid past a stretching wall. To answer this, the governing differential equation is derived by substituting similarity variables into the partial differential equations (PDEs) and associated boundary conditions. The present HBA is also developed by minimizing the averaged
more » ... e residual error included in the quadratic resistance law (QRL). By comparing the present findings with those available in the literature, it is seen that the 9th-order HBA can provide an incredible degree of accuracy and reliability. Furthermore, it is found that the central processing unit (CPU) time is greatly reduced when the auxiliary parameter is selected ash=-0.122.
doi:10.30538/psrp-easl2019.0022 fatcat:iqzkkwf5hrdjli5ectk66xnd4q

Solving a non-linear model of HIV infection for CD4+T cells by combining Laplace transformation and Homotopy analysis method [article]

Samad Noeiaghdam, Emran Khoshrouye Ghiasi
2019 arXiv   pre-print
The aim of this paper is to find the approximate solution of HIV infection model of CD4+T cells. For this reason, the homotopy analysis transform method (HATM) is applied. The presented method is combination of traditional homotopy analysis method (HAM) and the Laplace transformation. The convergence of presented method is discussed by preparing a theorem which shows the capabilities of method. The numerical results are shown for different values of iterations. Also, the regions of convergence
more » ... re demonstrated by plotting several h-curves. Furthermore in order to show the efficiency and accuracy of method, the residual error for different iterations are presented.
arXiv:1809.06232v2 fatcat:ef5pmo5fajccjixibhsi45yoty

Truncating the series expansion for unsteady velocity-dependent Eyring-Powell fluid

Emran Khoshrouye Ghiasi, Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran, Samad Noeiaghdam, South Ural State University, Lenin Prospect 76, Chelyabinsk, 454080, Russian Federation, Baikal School of BTICS, Irkutsk National Research Technical University, Irkutsk, Russian Federation
2020 Engineering and Applied Science Letters  
In this way, Khoshrouye Ghiasi and Saleh [12] employed a rather convergent feature of homotopy analysis method (HAM) by adding to the truncation technique, namely, tHAM, for solving the Falkner-Skan  ... 
doi:10.30538/psrp-easl2020.0049 fatcat:lhqlz6s4anbclgssbhm2prwzzi

A series solution for melting heat transfer characteristics of hybrid Casson fluid under thermal radiation

Emran Khoshrouye Ghiasi, Department of Mechanical Engineering, College of Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran, Reza Saleh, Department of Mechanical Engineering, College of Engineering, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2019 Engineering and Applied Science Letters  
Ghiasi and Saleh [2] analyzed the Casson type fluid over an unsteady shrinking surface in the presence of Joule heating and magnetic inclination.  ... 
doi:10.30538/psrp-easl2019.0028 fatcat:ddabquclfndrbfk4y3kesfihs4