Modified Variational Iteration Method for Traveling Wave Solutions of Seventh-order Generalized KdV Equations

2011 ◽  
Vol 12 (3) ◽  
pp. 107-113 ◽  
Author(s):  
Syed Tauseef Mohyud-Din ◽  
Muhammad Aslam Noor ◽  
Farah Jabeen
Keyword(s):  
Traveling Wave ◽  
Iteration Method ◽  
Traveling Wave Solutions ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Seventh Order ◽  
Generalized Kdv Equations ◽  
Modified Variational Iteration Method

TRAVELING WAVE SOLUTIONS OF SEVENTH-ORDER GENERALIZED KdV EQUATIONS BY VARIATIONAL ITERATION METHOD USING ADOMIAN'S POLYNOMIALS

2009 ◽  
Vol 23 (15) ◽  
pp. 3265-3277 ◽  
Author(s):  
SYED TAUSEEF MOHYUD-DIN ◽  
MUHAMMAD ASLAM NOOR ◽  
KHALIDA INAYAT NOOR
Keyword(s):  
Applied Sciences ◽  
Iteration Method ◽  
Traveling Wave Solutions ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Seventh Order ◽  
Generalized Kdv Equations ◽  
Adomian’S Polynomials

In this paper, we apply the variational iteration method using Adomian's polynomials (VIMAP) to investigate propagating traveling solitary wave solutions of seventh-order generalized KdV (SOG-KdV) equations, which play a very important role in mathematical physics, engineering, and applied sciences. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, perturbation, linearization, or restrictive assumptions and is formulated by the elegant coupling of variational iteration method and Adomian's polynomials.

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.

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