On the convergence of He's variational iteration method

By M. Tatari, Mehdi Dehghan. 2007

337 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/4001cd548ef4ff4e5eef858a69c313c5e079ebcd

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mechanics of Materials

1. Mehdi Dehghan
2. S. Yousefi
3. Ali Lotfi
4. Xu-Hong Wu
5. Mehrdad Lakestani
6. Abbas Saadatmandi
7. G. Domairry
8. Mahmoud Bayat

In Modeling and Simulation

1. Mehdi Dehghan
2. Mehrdad Lakestani
3. Jalil Manafian
4. Abbas Saadatmandi
5. S. Yousefi
6. Ali Lotfi
7. Mahmoud Bayat
8. I. Pakar

In Numerical Analysis

1. Mehdi Dehghan
2. Mehrdad Lakestani
3. S. Yousefi
4. Ali Lotfi
5. Abbas Saadatmandi
6. Jalil Manafian
7. G. Domairry
8. Mahmoud Bayat

Citations in the corpus

• Recent developments of some asymptotic methods and their applications for nonlinear vibration equations in engineering problems: a review (2012, methodology): “124 The VIM is useful to obtain exact and approximate solutions of linear and nonlinear differen125 tial equations [35, 57, 62, 99, 104, 117, 122, 136, 139, 153, 167, 177, 179, 184, 191, 202, 206].”
• An iterative approach for solving fractional optimal control problems (2018, neutral): “There are a few papers that verify the convergence of the VIM (Tatari and Dehghan, 2007; Salkuyeh, 2008; Odibat, 2010).”
• Alternative variational iteration method for solving the time-fractional Fornberg–Whitham equation (2015, positive): “Theorem 1 is a special case of the Banach fixed point theorem, which was used in [51] as a sufficient condition to study the convergence of the VIM for some partial differential equations.”
• Variational iteration method: New development and applications (2007, methodology): “[45] M. Tatari, M. Dehghan, He’s variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation, Chaos, Solitons and Fractals 33 (2) (2007) 671–677.”
• Application of variational iteration method for Hamilton–Jacobi–Bellman equations (2013, methodology): “Next theorem is a special case of Banach’s fixed point theorem which is used in [50], as a sufficient condition, to study the convergence of VIM for some partial differential equations [51].”
• THE CONSTRUCTION OF OPERATIONAL MATRIX OF FRACTIONAL DERIVATIVES USING B-SPLINE FUNCTIONS (2012, methodology): “Also we refer the interested reader to [8,9,39,41] for some basic ideas in Adomian decomposition method, the variational iteration method, homotopy perturbation method and the homotopy analysis method, respectively.”
• A spectral element approach for the stability of delay systems (2011, methodology): “Recently, the homotopy perturbation method (HPM) [18–21] and the variational iteration method (VIM) [21–24] were developed to find approximate analytical solutions for differential equations.”
• On the Variational Approach for Analyzing the Stability of Solutions of Evolution Equations (2013, background): “An alternative proof for the point wise-convergence theorem for the VIM had been given in [24].”
• Solving nonlinear fractional partial differential equations using the homotopy analysis method (2010, methodology): “Wazwaz [23], examined the KdV, the K(2, 2), the Burgers, and the cubic Boussinesq equations by using variational iteration method (VIM) [40–51].”
• The use of He's variational iteration method for solving the telegraph and fractional telegraph equations (2011, methodology): “In [29] a convergence criterion based on Banach fixed point is given for this method.”