Numerical solution of sine-Gordon equation by variational iteration method

2007 ◽  
Vol 370 (5-6) ◽  
pp. 437-440 ◽  
Author(s):  
B. Batiha ◽  
M.S.M. Noorani ◽  
I. Hashim
Keyword(s):  
Numerical Solution ◽  
Iteration Method ◽  
Gordon Equation ◽  
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.

Numerical solution of the general Volterra nth-order integro-differential equations via variational iteration method

2018 ◽  
Vol 13 (02) ◽  
pp. 2050042
Author(s):  
Fernane Khaireddine
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Numerical Solution ◽  
General Formula ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Numerical Examples ◽  
Variational Iteration ◽  
Linear And Nonlinear

In this paper, we use the variational iteration method (VIM) to construct approximate solutions for the general [Formula: see text]th-order integro-differential equations. We show that his method can be effectively and easily used to solve some classes of linear and nonlinear Volterra integro-differential equations. Finally, some numerical examples with exact solutions are given.

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