A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials

By Saeid Abbasbandy. 2007

290 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/592920fbdf89a7728d604bb6419301916265ceaa

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Citations in the corpus

The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method (2013, methodology): “Notably, implementations of difference methods such as in the differential transform method (DTM), the Adomian decomposition method (ADM) [30–33], the variational iteration method (VIM) [34–40] empowered us to achieve approximate solutions of various ordinary differential equations.”
Numerical Solution of Bratu-type Equations by the Variational Iteration Method (2010, unknown): “Abbasbandy [1] solved one example of the quadratic Riccati differential equation (with constant coefficient) by He’s variational iteration method by using Adomian’s polynomials.”
Variational iteration method: New development and applications (2007, methodology): “In order to accelerate the convergent rate, various other modifications were suggested, for example variational iteration–Pade method [51], variational iteration–Adomian method [16], variational iteration–differential transform method [52].”
DIFFERENTIAL TRANSFORM METHOD FOR QUADRATIC RICCATI DIFFERENTIAL EQUATION (2010, methodology): “Abbasbandy [9] solved one example of the quadratic Riccati differential equation (with constant coefficient) by He’s variational iteration method by using Adomian’s polynomials.”
Challenge in the variational iteration method – A new approach to identification of the Lagrange multipliers (2013, background): “2.12.002 lsevier a relatively fledged theory thanks to the efforts of many researchers, notably (Abbasbandy, 2007; Noor and MohyudDin, 2008; Xu, 2009; Geng, 2010; Jafari and Khalique, 2012) to mention only a few.”
Variational Iteration Method for Solving Higher-order Nonlinear Boundary Value Problems Using He's Polynomials (2008, methodology): “In this technique, the correction functional is developed [1, 2, 16-25, 32-37, 42] and the Lagrange multipliers are calculated optimally via variational theory.”
Variational Iteration Decomposition Method for Solving Eighth-Order Boundary Value Problems (2007, methodology): “In this paper, we have used the variational iteration decomposition method (VIDM) which is mainly due to Abbasbandy for finding the solution of linear and nonlinear boundary value problems for eighth order.”