scholarly journals An analytical approach to fractional Bousinesq-Burges equations

2020 ◽  
Vol 24 (4) ◽  
pp. 2581-2588
Author(s):  
Feng Lu
Keyword(s):  
Fractional Calculus ◽  
Iteration Method ◽  
Analytical Approach ◽  
Variational Iteration Method ◽  
Fractional Complex Transform ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

This paper proposes an analytical approach to fractional calculus by the fractional complex transform and the modified variational iteration method. The fractional Bousinesq-Burges equations are used as an example to reveal the main merits of the present technology.

scholarly journals Analytical approach to a generalized Hirota-Satsuma coupled Korteweg-de Vries equation by modified variational iteration method

2016 ◽  
Vol 20 (3) ◽  
pp. 885-888 ◽  
Author(s):  
Jun-Feng Lu ◽  
Li Ma
Keyword(s):  
Iteration Method ◽  
Analytical Approach ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
De Vries ◽  
Modified Variational Iteration Method

In this paper, we apply the modified variational iteration method to a generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) equation. The numerical solutions of the initial value problem of the generalized Hirota-Satsuma coupled KdV equation are provided. Numerical results are given to show the efficiency of the modified variational iteration method.

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

2013 ◽  
Vol 16 (1) ◽  
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.

A NEWLY MODIFIED VARIATIONAL ITERATION METHOD FOR SOLVING NONLINEAR DIFFERENTIAL EQUATIONS

2013 ◽  
Vol 10 (05) ◽  
pp. 1350029
Author(s):  
R. YULITA MOLLIQ ◽  
M. S. M. NOORANI
Keyword(s):  
Iteration Method ◽  
Nonlinear Differential Equations ◽  
Method Comparison ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Accurate Method ◽  
Convergence Region ◽  
Variational Iteration ◽  
Approximate Analytical Solutions ◽  
Modified Variational Iteration Method

This paper presents a new reliable modification of the variational iteration method (MoVIM). An enlarged interval of convergence region of series solutions is obtained by inserting a nonzero auxiliary parameter (ℏ) into the correction functional of variational iteration method. Approximate analytical solutions for some examples of nonlinear problems are obtained using variational iteration method. Comparison with the exact solution, Runge–Kutta method 4, and also another modified variational iteration method has shown that MoVIM is an accurate method for solving nonlinear problems.

scholarly journals Approximate Solution of Linear Fuzzy Initial Value Problems Using Modified Variaional Iteration Method

2021 ◽  
Vol 24 (4) ◽  
pp. 32-39
Author(s):  
Hussein M. Sagban ◽  
◽  
Fadhel S. Fadhel ◽  
Keyword(s):  
Approximate Solution ◽  
Rate Of Convergence ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

The main objective of this paper is to solve fuzzy initial value problems, in which the fuzziness occurs in the initial conditions. The proposed approach, namely the modified variational iteration method, will be used to find the solution of fuzzy initial value problem approximately and to increase the rate of convergence of the variational iteration method. From the obtained results, as it is expected, the approximate results of the proposed method are more accurate than those results obtained without using the modified variational iteration method.

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