Approximate analytical solution of the coupled sine-Gordon equation using the variational iteration method

2007 ◽  
Vol 76 (5) ◽  
pp. 445-448 ◽  
Author(s):  
B Batiha ◽  
M S M Noorani ◽  
I Hashim
Keyword(s):  
Analytical Solution ◽  
Iteration Method ◽  
Gordon Equation ◽  
Approximate Analytical Solution ◽  
Variational Iteration Method ◽  
Sine Gordon Equation ◽  
Variational Iteration

scholarly journals New Solution of the Sine-Gordon Equation by the Daftardar-Gejji and Jafari Method

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 57
Author(s):  
Belal Batiha
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Iteration Method ◽  
Gordon Equation ◽  
Approximate Analytical Solution ◽  
Variational Iteration Method ◽  
Comparison Study ◽  
Sine Gordon Equation ◽  
Variational Iteration

In this article, the Daftardar-Gejji and Jafari method (DJM) is used to obtain an approximate analytical solution of the sine-Gordon equation. Some examples are solved to demonstrate the accuracy of DJM. A comparison study between DJM, the variational iteration method (VIM), and the exact solution are presented. The comparison of the present symmetrical results with the existing literature is satisfactory.

scholarly journals Analytical solution to local fractional Landau-Ginzburg-Higgs equation on fractal media

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4449-4455
Author(s):  
Shu-Xian Deng ◽  
Xin-Xin Ge
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Present Article ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Fractal Media

The main objective of the present article is to introduce a new analytical solution of the local fractional Landau-Ginzburg-Higgs equation on fractal media by means of the local fractional variational iteration transform method, which is coupling of the variational iteration method and Yang-Laplace transform method.

scholarly journals Variational Iteration Method for Analytical Solution of the Lane-Emden Type Equation with Singular Initial and Boundary Conditions

2019 ◽  
pp. 127-142 ◽  
Author(s):  
Muhammad Nadeem ◽  
Hijaz Ahmad
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Type Equation ◽  
Variational Iteration Method ◽  
Mathematical Physics ◽  
Initial Value ◽  
Emden Equation ◽  
Variational Iteration

In this paper, a well-known equation used in astrophysics and mathematical physics called the Lane-Emden equation is to be solved by a variational iteration method. The main purpose of this approach is to solve the singular initial value problems and also boundary value problem of Lane-Emden type equations. This technique overcomes its singularity at origin rapidly. It gives the approximate and exact solution with easily computable terms. The approach is illustrated with some examples to show its reliability and compactness.

scholarly journals He’s fractal calculus and its application to fractal KdV equation

2021 ◽  
pp. 100-100
Author(s):  
Xue-Si Ma ◽  
Li-Na Zhang
Keyword(s):  
Analytical Solution ◽  
Iteration Method ◽  
Approximate Analytical Solution ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Natural Phenomena ◽  
Transform Method ◽  
Fractal Derivative ◽  
Fractal Calculus ◽  
Fractal Space

He?s fractal calculus is a powerful and effective tool to dealing with natural phenomena in a fractal space. In this paper, we study the fractal KdV equation with He?s fractal derivative. We first adopt the two-scale transform method to convert the fractal KdV equation into its traditional partner in acontinuous space. Finally, we successfully use He?s variational iteration method (HVIM) to obtain its approximate analytical solution.

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