The Experts below are selected from a list of 125451 Experts worldwide ranked by ideXlab platform
Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.
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accelerated double step scale splitting Iteration Method for solving a class of complex symmetric linear systems
Numerical Algorithms, 2020Co-Authors: Mehdi Dehghan, Akbar ShirilordAbstract:In this paper, we introduce and study an accelerated double-step scale splitting (ADSS) Iteration Method for solving complex linear systems. The convergence of the ADSS Iteration Method is determined under suitable conditions. Also each Iteration of ADSS Method requires the solution of two linear systems that their coefficient matrices are real symmetric positive definite. We analytically prove that the ADSS Iteration Method is faster than the DSS Iteration Method. Moreover, to increase the convergence rate of this Method, we minimize the upper bound of the spectral radius of Iteration matrix. Finally, some test problems will be given and simulation results will be reported to support the theoretical results.
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variational Iteration Method for solving a generalized pantograph equation
Computers & Mathematics With Applications, 2009Co-Authors: Abbas Saadatmandi, Mehdi DehghanAbstract:The variational Iteration Method is applied to solve the generalized pantograph equation. This technique provides a sequence of functions which converges to the exact solution of the problem and is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. Employing this technique, it is possible to find the exact solution or an approximate solution of the problem. Some examples are given to demonstrate the validity and applicability of the Method and a comparison is made with existing results.
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on the convergence of he s variational Iteration Method
Journal of Computational and Applied Mathematics, 2007Co-Authors: Mehdi Tatari, Mehdi DehghanAbstract:In this work we will consider He's variational Iteration Method for solving second-order initial value problems. We will discuss the use of this approach for solving several important partial differential equations. This Method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This procedure is a powerful tool for solving the large amount of problems. Using the variational Iteration Method, it is possible to find the exact solution or an approximate solution of the problem. This technique provides a sequence of functions which converges to the exact solution of the problem. Our emphasis will be on the convergence of the variational Iteration Method. In the current paper this scheme will be investigated in details and efficiency of the approach will be shown by applying the procedure on several interesting and important models.
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he s variational Iteration Method for computing a control parameter in a semi linear inverse parabolic equation
Chaos Solitons & Fractals, 2007Co-Authors: Mehdi Tatari, Mehdi DehghanAbstract:Abstract In this work the well known variational Iteration Method is used for finding the solution of a semi-linear inverse parabolic equation. This Method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a functional. Using this Method a rapid convergent sequence is produced which tends to the exact solution of the problem. Thus the variational Iteration Method is suitable for finding the approximation of the solution without discretization of the problem. We will change the main problem to a direct problem which is easy to handle the variational Iteration Method. To show the efficiency of the present Method, several examples are presented. Also it is shown that this Method coincides with Adomian decomposition Method for the studied problem.
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numerical solution of the klein gordon equation via he s variational Iteration Method
Nonlinear Dynamics, 2007Co-Authors: Fatemeh Shakeri, Mehdi DehghanAbstract:In this paper, we present the solution of the Klein--Gordon equation. Klein--Gordon equation is the relativistic version of the Schrodinger equation, which is used to describe spinless particles. The He’s variational Iteration Method (VIM) is implemented to give approximate and analytical solutions for this equation. The variational Iteration Method is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. Application of variational Iteration technique to this problem shows rapid convergence of the sequence constructed by this Method to the exact solution. Moreover, this technique reduces the volume of calculations by avoiding discretization of the variables, linearization or small perturbations.
Klaus-jürgen Bathe - One of the best experts on this subject based on the ideXlab platform.
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The subspace Iteration Method - Revisited
Computers & Structures, 2013Co-Authors: Klaus-jürgen BatheAbstract:The objective in this paper is to present some recent developments regarding the subspace Iteration Method for the solution of frequencies and mode shapes. The developments pertain to speeding up the basic subspace Iteration Method by choosing an effective number of Iteration vectors and by the use of parallel processing. The subspace Iteration Method lends itself particularly well to shared and distributed memory processing. We present the algorithms used and illustrative sample solutions. The present paper may be regarded as an addendum to the publications presented in the early 1970s, see Refs. [1,2], taking into account the changes in computers that have taken place.
Abdulmajid Wazwaz - One of the best experts on this subject based on the ideXlab platform.
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the variational Iteration Method for solving nonlinear singular boundary value problems arising in various physical models
Communications in Nonlinear Science and Numerical Simulation, 2011Co-Authors: Abdulmajid WazwazAbstract:Abstract In this paper, the variational Iteration Method (VIM) is used to study a nonlinear singular boundary value problems arising in various physical equations. The VIM overcomes the singularity issue at the origin x = 0. The Lagrange multipliers for all four cases of the boundary value problems are formally derived. The variational Iteration Method is tested for its efficiency and reliability.
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a study on linear and nonlinear schrodinger equations by the variational Iteration Method
Chaos Solitons & Fractals, 2008Co-Authors: Abdulmajid WazwazAbstract:Abstract In this work, we introduce a framework to obtain exact solutions to linear and nonlinear Schrodinger equations. The He’s variational Iteration Method (VIM) is used for analytic treatment of these equations. Numerical examples are tested to show the pertinent features of this Method.
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a comparison between the variational Iteration Method and adomian decomposition Method
Journal of Computational and Applied Mathematics, 2007Co-Authors: Abdulmajid WazwazAbstract:In this paper, we present a comparative study between the variational Iteration Method and Adomian decomposition Method. The study outlines the significant features of the two Methods. The analysis will be illustrated by investigating the homogeneous and the nonhomogeneous advection problems.
Ishak Hashim - One of the best experts on this subject based on the ideXlab platform.
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on solving the chaotic chen system a new time marching design for the variational Iteration Method using adomian s polynomial
Numerical Algorithms, 2010Co-Authors: S M Goh, Mohd Salmi Md Noorani, Ishak HashimAbstract:This paper centres on the effectiveness of the variational Iteration Method and its modifications for numerically solving the chaotic Chen system, which is a three-dimensional system of ODEs with quadratic nonlinearities. This research implements the multistage variational Iteration Method with an emphasis on the new multistage hybrid of variational Iteration Method with Adomian polynomials. Numerical comparisons are made between the multistage variational Iteration Method, the multistage variational Iteration Method using the Adomian’s polynomials and the classic fourth-order Runge-Kutta Method. Our work shows that the new multistage hybrid provides good accuracy and efficiency with a performance that surpasses that of the multistage variational Iteration Method.
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variational Iteration Method for fractional heat and wave like equations
Nonlinear Analysis-real World Applications, 2009Co-Authors: Yulita Molliq R, Mohd Salmi Md Noorani, Ishak HashimAbstract:This paper applies the variational Iteration Method to obtaining analytical solutions of fractional heat- and wave-like equations with variable coefficients. Comparison with the Adomian decomposition Method shows that the VIM is a powerful Method for the solution of linear and nonlinear fractional differential equations.
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numerical solution of sine gordon equation by variational Iteration Method
Physics Letters A, 2007Co-Authors: B Batiha, Mohd Salmi Md Noorani, Ishak HashimAbstract:In this Letter, variational Iteration Method (VIM) is applied to obtain approximate analytical solution of the sine-Gordon equation without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.
Dumitru Baleanu - One of the best experts on this subject based on the ideXlab platform.
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local fractional variational Iteration Method for diffusion and wave equations on cantor sets
2014Co-Authors: Xiaojun Yang, Dumitru Baleanu, Yasir Khan, Syed Tauseef Mohyuddin, Saudi ArabiaAbstract:In this work, the local fractional variational Iteration Method is employed to handle the sub-diffusion and wave equations and the analytical solutions are obtained. The present Method is efficient and implicit to investigate the differential equations with the local fractional derivatives.
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damped wave equation and dissipative wave equation in fractal strings within the local fractional variational Iteration Method
Fixed Point Theory and Applications, 2013Co-Authors: Xiaojun Yang, Dumitru Baleanu, Hossein JafariAbstract:In this paper, the local fractional variational Iteration Method is given to handle the damped wave equation and dissipative wave equation in fractal strings. The approximation solutions show that the Methodology of local fractional variational Iteration Method is an efficient and simple tool for solving mathematical problems arising in fractal wave motions. MSC: 74H10; 35L05; 28A80
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variational Iteration Method for fractional calculus a universal approach by laplace transform
Advances in Difference Equations, 2013Co-Authors: Guocheng Wu, Dumitru BaleanuAbstract:A novel modification of the variational Iteration Method (VIM) is proposed by means of the Laplace transform. Then the Method is successfully extended to fractional differential equations. Several linear fractional differential equations are analytically solved as examples and the Methodology is demonstrated. MSC: 39A08, 65K10, 34A12.
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fractal heat conduction problem solved by local fractional variation Iteration Method
Thermal Science, 2013Co-Authors: Xiaojun Yang, Dumitru BaleanuAbstract:This paper points out a novel local fractional variational Iteration Method for processing the local fractional heat conduction equation arising in fractal heat transfer.
