Modified variational iteration method for solving a neutral functional‐differential equation with proportional delays

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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Extension of Zhou's Method to Neutral Functional-Differential Equation with Proportional Delays

ISRN Applied Mathematics ◽

10.5402/2012/518361 ◽

2012 ◽

Vol 2012 ◽

pp. 1-10 ◽

Cited By ~ 1

Author(s):

Sabir Widatalla

Keyword(s):

Differential Equation ◽

Functional Differential Equation ◽

Reliable Method ◽

Approximate Solutions ◽

Neutral Functional Differential Equation ◽

Transform Method ◽

Proportional Delays ◽

Differential Transform ◽

Functional Differential ◽

Good Agreement

The differential transform method (DTM) is a reliable method applied by providing new theorems to develop exact and approximate solutions of neutral functional-differential equation (NFDE) with proportional delays. The results obtained with the proposed methods are in good agreement with one obtained by other methods. The advantages of this technique are illustrated. It is easy to see that the DTM is very accurate and easy to implement in finding analytical solutions of wide classes of linear and nonlinear NFDEs.

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

Thermal Science ◽

10.2298/tsci170612269d ◽

2018 ◽

Vol 22 (Suppl. 1) ◽

pp. 33-46 ◽

Cited By ~ 7

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.

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