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

2009 ◽  
Vol 64 (12) ◽  
pp. 783-787 ◽  
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

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

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
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.

scholarly journals Application of He's Variational Iteration Method to Solve Semidifferential Equations of th Order

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Asghar Ghorbani ◽  
Abdolsaeed Alavi
Keyword(s):  
Iteration Method ◽  
Present Method ◽  
Variational Iteration Method ◽  
Convergent Series ◽  
Mathematical Tool ◽  
Spline Method ◽  
Weak Nonlinearity ◽  
Variational Iteration ◽  
He’S Variational Iteration Method ◽  
Powerful Mathematical Tool

He's variational iteration method is applied to solve th order semidifferential equations. Comparison is made between collocation spline method based on Lagrange interpolation and the present method. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions, or perturbation theory. Some examples are given to illustrate the effectiveness of the method; the results show that He's method provides a straightforward and powerful mathematical tool for solving various semidifferential equations of the th order.

scholarly journals Fractional variational iteration method for time-fractional non-linear functional partial differential equation having proportional delays

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 33-46 ◽  
Author(s):  
Durgun Dogan ◽  
Ali Konuralp
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Iteration Method ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Partial Differential ◽  
Data Set ◽  
Proportional Delays ◽  
Variational Iteration ◽  
Non Linear

In this paper, time-fractional non-linear partial differential equation with proportional delays are solved by fractional variational iteration method taking into account modified Riemann-Liouville fractional derivative. The numerical solutions which are calculated by using this method are better than those obtained by homotopy perturbation method and differential transform method with same data set and approximation order. On the other hand, to improve the solutions obtained by fractional variational iteration method, residual error function is used. With this additional process, the resulting approximate solutions are getting closer to the exact solutions. The results obtained by taking into account different values of variables in the domain are supported by compared tables and graphics in detail.

scholarly journals He's Variational Iteration Method for Solving Fractional Riccati Differential Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
H. Jafari ◽  
H. Tajadodi
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Iteration Method ◽  
Present Method ◽  
Variational Iteration Method ◽  
Riccati Differential Equation ◽  
Variational Iteration ◽  
Optimal Value ◽  
He’S Variational Iteration Method ◽  
Sequence Of Functions

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.

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

2010 ◽  
Vol 65 (5) ◽  
pp. 418-430 ◽  
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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