• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.381-394
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• 2011

In this paper, a Naveir-Stokes equation is solved by using the Adomian's decomposition method (ADM), modified Adomian's decomposition method (MADM), variational iteration method (VIM), modified variational iteration method (MVIM), modified homotopy perturbation method (MHPM) and homotopy analysis method (HAM). The approximate solution of this equation is calculated in the form of series which its components are computed by applying a recursive relation. The existence and uniqueness of the solution and the convergence of the proposed methods are proved. A numerical example is studied to demonstrate the accuracy of the presented methods.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.141-154
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• 2024

This article offers a thorough exploration of a modified Black-Scholes model featuring two assets. The determination of option prices is accomplished through the Black-Scholes partial differential equation, leveraging the variational iteration method. This approach represents a semi-analytical technique that incorporates the use of Lagrange multipliers. The Lagrange multiplier emerges as a beacon of efficiency, adeptly streamlining the computational intricacies, and elevating the model's efficacy to unprecedented heights. For better understanding of the presented system, a graphical and tabular interpretation is presented with the help of Maple software.

• Nonlinear Functional Analysis and Applications
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• v.27 no.1
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• pp.189-201
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• 2022

The aim of the current work is to investigate the numerical study of a nonlinear Volterra-Fredholm integro-differential equation with initial conditions. Our approximation techniques modified adomian decomposition method (MADM) and variational iteration method (VIM) are based on the product integration methods in conjunction with iterative schemes. The convergence of the proposed methods have been proved. We conclude the paper with numerical examples to illustrate the effectiveness of our methods.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.673-710
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• 2024

In this paper, we propose a modified Halpern's iterative scheme developed from a sequence of a new class of enriched nonspreading mappings and an enriched nonexpansive mapping in the setup of a real Hilbert space. Moreover, we prove strong convergence theorem of the proposed method under mild conditions on the control parameters. Also, we obtain some basic properties of our new class of enriched nonspreading mappings.

• Steel and Composite Structures
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• v.24 no.1
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• pp.65-77
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• 2017

The purpose of this research is to study the nonlinear free vibration and post-buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beams resting on a nonlinear elastic foundation. Uniformly and functionally graded distributions of single walled carbon nanotubes as reinforcing phase are considered in the polymeric matrix. The modified form of rule of mixture is used to estimate the material properties of CNTRC beams. The governing equations are derived employing Euler-Bernoulli beam theory along with energy method and Hamilton's principle. Applying von $K\acute{a}rm\acute{a}n's$ strain-displacement assumptions, the geometric nonlinearity is taken into consideration. The developed governing equations with quadratic and cubic nonlinearities are solved using variational iteration method (VIM) and the analytical expressions and numerical results are obtained for vibration and stability analysis of nanocomposite beams. The presented comparative results are indicative for the reliability, accuracy and fast convergence rate of the solution. Eventually, the effects of different parameters, such as foundation stiffness, volume fraction and distributions of carbon nanotubes, slenderness ratio, vibration amplitude, coefficients of elastic foundation and boundary conditions on the nonlinear frequencies, vibration response and post-buckling loads of FG-CNTRC beams are examined. The developed analytical solution provides direct insight into parametric studies of particular parameters of the problem.