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

We will consider He's variational iteration method for solving fractional Riccati differential equation. This method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. This technique provides a sequence of functions which converges to the exact solution of the problem. The present method performs extremely well in terms of efficiency and simplicity.

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A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-013-0008-9 ◽

2013 ◽

Vol 16 (1) ◽

Cited By ~ 33

Author(s):

Hossein Jafari ◽

Hale Tajadodi ◽

Dumitru Baleanu

Keyword(s):

Differential Equation ◽

Iteration Method ◽

Variational Iteration Method ◽

Approximate Solutions ◽

Convergence Region ◽

Riccati Differential Equation ◽

Adomian Polynomials ◽

Riccati Differential Equations ◽

Variational Iteration ◽

Modified Variational Iteration Method

AbstractIn this paper, we introduce a modified variational iteration method (MVIM) for solving Riccati differential equations. Also the fractional Riccati differential equation is solved by variational iteration method with considering Adomians polynomials for nonlinear terms. The main advantage of the MVIM is that it can enlarge the convergence region of iterative approximate solutions. Hence, the solutions obtained using the MVIM give good approximations for a larger interval. The numerical results show that the method is simple and effective.

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He’s Variational Iteration Method for Solving a Partial Differential Equation Arising in Modelling of theWater Waves

Zeitschrift für Naturforschung A ◽

10.1515/zna-2009-1202 ◽

2009 ◽

Vol 64 (12) ◽

pp. 783-787 ◽

Cited By ~ 10

Author(s):

Abbas Saadatmandi ◽

Mehdi Dehghan

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Small Perturbation ◽

Efficient Method ◽

Iteration Method ◽

Variational Iteration Method ◽

Convergent Series ◽

Kawahara Equation ◽

Variational Iteration ◽

He’S Variational Iteration Method

The variational iteration method is applied to solve the Kawahara equation. This method produces the solutions in terms of convergent series and does not require linearization or small perturbation. Some examples are given. The comparison with the theoretical solution shows that the variational iteration method is an efficient method

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Application of He’s Variational Iteration Method to Nonlinear Integro-Differential Equations

Zeitschrift für Naturforschung A ◽

10.1515/zna-2010-0507 ◽

2010 ◽

Vol 65 (5) ◽

pp. 418-430 ◽

Cited By ~ 1

Author(s):

Ahmet Yildirim

Keyword(s):

Differential Equations ◽

Iteration Method ◽

Variational Iteration Method ◽

Mathematical Tool ◽

Variational Iteration ◽

He’S Variational Iteration Method ◽

Powerful Mathematical Tool

In this paper, an application of He’s variational iteration method is applied to solve nonlinear integro-differential equations. Some examples are given to illustrate the effectiveness of the method. The results show that the method provides a straightforward and powerful mathematical tool for solving various nonlinear integro-differential equations

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Numerical simulation of the generalized Huxley equation by He’s variational iteration method

Applied Mathematics and Computation ◽

10.1016/j.amc.2006.07.166 ◽

2007 ◽

Vol 186 (2) ◽

pp. 1322-1325 ◽

Cited By ~ 26

Author(s):

B. Batiha ◽

M.S.M. Noorani ◽

I. Hashim

Keyword(s):

Numerical Simulation ◽

Iteration Method ◽

Variational Iteration Method ◽

Variational Iteration ◽

Huxley Equation ◽

He’S Variational Iteration Method

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Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

Mathematical Problems in Engineering ◽

10.1155/2015/573932 ◽

2015 ◽

Vol 2015 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Guanglu Zhou ◽

Boying Wu ◽

Wen Ji ◽

Seungmin Rho

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Inverse Problem ◽

Iteration Method ◽

Numerical Experiments ◽

Sensor Array ◽

Variational Iteration Method ◽

Parabolic Partial Differential Equation ◽

Partial Differential ◽

Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

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