• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.177-189
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• 2024

In this paper, we suggest and analyze new higher order classes of iterative methods for solving nonlinear equations by using variational iteration technique. We present several examples to illustrate the efficiency of the proposed methods. Comparison with other similar methods is also given. New methods can be considered as an alternative of the existing methods. This technique can be used to suggest a wide class of new iterative methods for solving nonlinear equations.

• 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.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1343-1359
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• 2009

In this paper, we implement a relatively new analytical technique by combining the traditional variational iteration method and the decomposition method which is called as the variational decomposition method (VDM) for solving the sixth-order boundary value problems. The proposed technique is in fact the modification of variatioanal iteration method by coupling it with the so-called Adomian's polynomials. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Comparisons are made to verify the reliability and accuracy of the proposed algorithm. Several examples are given to check the efficiency of the proposed algorithm. We have also considered an example where the VDM is not reliable.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.733-745
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• 2013

In this paper, we first propose a new technique of the functional iterative methods VIM (Variational iteration method) and NHPM (New homotopy perturbation method) for solving two-point boundary value problems, and then we compare their numerical results with those of the finite difference method (FDM).

• Journal of KSNVE
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• v.10 no.2
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• pp.319-324
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• 2000

This paper shows hot to model the submerged elastic structures and adequate analysis tools for modal behavior when using finite element and boundary element method. Four different cases are reviewed depending on the location of the water and air. First case is that structures are filled with air and water is located outside. Second case is opposite to case one. These cases are solved by direct approach using collocation procedure. Third case is that water is located both sides of structures. Last case is that air is located both sides. These cases are solved by indirect approach using variational procedure. As analysis tools harmonic frequency sweep analysis and eigenvalue iteration method are selected to obtain the natural frequencies of vibrating submerged structures depending on the cases. Results are compared with closed form solutions of submerged spherical shell.