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 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.

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 Solving Two Dimensional Coupled Burger's Equations and Sine-Gordon Equation Using El-Zaki Transform-Variational Iteration Method

2021 ◽  
Vol 24 (2) ◽  
pp. 41-47
Author(s):  
Marwa H. Al-Tai ◽  
◽  
Ali Al-Fayadh ◽  
Keyword(s):  
Differential Equation ◽  
Iteration Method ◽  
Gordon Equation ◽  
Numerical Solutions ◽  
Variational Iteration Method ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
Partial Differential ◽  
Burger's Equations ◽  
Variation Iteration Method

In this paper, the combined form of the Elzaki transform and variation iteration method is implemented efficiently in finding the analytical and numerical solutions of the two-dimensional nonlinear coupled Burger's partial differential equations and sine-Gordon partial differential equation. The obtained solutions were compared to the exact solutions and other existing methods. Illustrative examples show the efficiency and the power of the used method.

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