Browsing by Author "Ghaderi, P."

Now showing 1 - 5 of 5

Citation - WoS: 5
Citation - Scopus: 6
Analytic Solution for a Nonlinear Problem of Magneto-Thermoelasticity
(Pergamon-elsevier Science Ltd, 2013) Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; Jafarian, A.
In this paper, we present a comparative study of the homotopy analysis method (HAM), the variational iteration method (VIM) and the iterative method (He's polynomials). The approximate solution of the coupled harmonic waves nonlinear magneto-thermoelasticity equations under influence of rotation is obtained. In order to control and adjust the convergence region and the rate of solution series, we show that it is possible to choose a valid auxiliary parameter h of HAM. Using the boundary and the initial conditions we select a suitable initial approximation. The results show that these methods are very efficient, convenient and applicable to a large class of problems.
Citation - WoS: 20
Citation - Scopus: 21
Analytical Approximate Solutions of the Zakharov-Kuznetsov Equations
(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; Matematik
In this paper, analytical approximate solutions for the Zakharov-Kuznetsov equations by homotopy analysis method (HAM) and the He's polynomials iterative method (HPIM) are presented. Our results indicate the remarkable efficiency of HAM as compared to HPIM. The convergence of these two methods is also analyzed.
Citation - WoS: 20
Citation - Scopus: 22
Analytical Treatment of System of Abel Integral Equations by Homotopy Analysis Method
(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; Matematik
Abel equation has important applications in describing the least time for an object which is sliding on surface without friction in uniform gravity, and the classical theory of elasticity of materials is modeled by a system of Abel integral equations. In this manuscript, the homotopy analysis method is presented for obtaining analytical solutions of a system of Abel integral equations as fractional equations. The applied method has lessened the size of calculation and improved the accuracy of solution in the case of the singular Abel integral equation. The illustrated examples and numerical results have proved the assertion.
Citation - WoS: 20
Homotopy Analysis Method for Solving Coupled Ramani Equations
(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; Matematik
In this manuscript, coupled Ramani equations are solved by means of an analytic technique, namely the homotopy analysis method (HAM). The HAM is a capable and a straightforward analytic tool for solving nonlinear problems and does not need small parameters in the governing equations and boundary/initial conditions. The result of this study presents the utility and sufficiency of HAM method. Comparisons demonstrate that there is a good agreement between the HAM solutions and the exact solutions.
Citation - WoS: 14
Citation - Scopus: 16
On a One-Dimensional Nonlinear Coupled System of Equations in the Theory of Thermo Elasticity
(Editura Acad Romane, 2013) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, A.K.; Baleanu, D.; Golmanichaneh, Alireza K.; Matematik
The thermoelasticity deals with predicting the thermo mechanical treatment of elastic solids and it is a generalization of the classical theory of elasticity and the theory of thermal conductivity. In this manuscript, the system of nonlinear partial differential equations such as the Cauchy problem which appears in a one-dimensional nonlinear coupled system of equations in the theory of thermo elasticity is studied. The homotopy analysis method was used to perform successfully the numerical calculations.