scholarly journals Variational iteration method for the classical Drinfel’d-Sokolov-Wilson equation

2014 ◽  
Vol 18 (5) ◽  
pp. 1543-1546 ◽  
Author(s):  
Lin Jin ◽  
Jun-Feng Lu
Keyword(s):  
Initial Value Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Variational Iteration Method ◽  
Wilson Equation ◽  
Initial Value ◽  
Variational Iteration

In this paper, we apply the variational iteration method to solve the classical Drinfel?d-Sokolov-Wilson equation. The initial value problem of the classical Drinfel?d-Sokolov-Wilson equation is considered. Numerical experiments are presented to show the efficiency of the method.

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.

scholarly journals Numerical Simulation of the FitzHugh-Nagumo Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. A. Soliman
Keyword(s):  
Numerical Simulation ◽  
Initial Value Problem ◽  
Iteration Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Initial Value ◽  
Variational Iteration ◽  
Adomian Decomposition ◽  
Nagumo Equations

The variational iteration method and Adomian decomposition method are applied to solve the FitzHugh-Nagumo (FN) equations. The two algorithms are illustrated by studying an initial value problem. The obtained results show that only few terms are required to deduce approximated solutions which are found to be accurate and efficient.

scholarly journals Modified variational iteration method for variant Boussinesq equation

2015 ◽  
Vol 19 (4) ◽  
pp. 1195-1199 ◽  
Author(s):  
Jun-Feng Lu
Keyword(s):  
Exact Solutions ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Numerical Experiments ◽  
Boussinesq Equation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Initial Value ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

In this paper, we solve the variant Boussinesq equation by the modified variational iteration method. The approximate solutions to the initial value problems of the variant Boussinesq equation are provided, and compared with the exact solutions. Numerical experiments show that the modified variational iteration method is efficient for solving the variant Boussinesq equation.

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

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.

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