Approximate solution of a differential equation arising in astrophysics using the variational iteration method

New Astronomy ◽  
2008 ◽  
Vol 13 (1) ◽  
pp. 53-59 ◽  
Author(s):  
Mehdi Dehghan ◽  
Fatemeh Shakeri
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Variational Iteration

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.

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.

scholarly journals The Approximate Solution of Fractional Fredholm Integrodifferential Equations by Variational Iteration and Homotopy Perturbation Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Perturbation Methods ◽  
Variational Iteration Method ◽  
Integrodifferential Equations ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Constant Coefficients

Variational iteration method and homotopy perturbation method are used to solve the fractional Fredholm integrodifferential equations with constant coefficients. The obtained results indicate that the method is efficient and also accurate.

scholarly journals Variational Iteration Method for Solving the Generalized Degasperis-Procesi Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qian Lijuan ◽  
Tian Lixin ◽  
Ma Kaiping
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Initial Approximation ◽  
Variational Iteration Method ◽  
Original Equation ◽  
Variational Iteration

We introduce the variational iteration method for solving the generalized Degasperis-Procesi equation. Firstly, according to the variational iteration, the Lagrange multiplier is found after making the correction functional. Furthermore, several approximations ofun+1(x,t)which is converged tou(x,t)are obtained, and the exact solutions of Degasperis-Procesi equation will be obtained by using the traditional variational iteration method with a suitable initial approximationu0(x,t). Finally, after giving the perturbation item, the approximate solution for original equation will be expressed specifically.

The Variational-Iteration Method to Solve the Nonlinear Boltzmann Equation

2008 ◽  
Vol 63 (3-4) ◽  
pp. 131-139 ◽  
Author(s):  
Essam M. Abulwafa ◽  
Mohammed A. Abdou ◽  
Aber H. Mahmoud
Keyword(s):  
Differential Equation ◽  
Distribution Function ◽  
Boltzmann Equation ◽  
Generating Function ◽  
Iteration Method ◽  
Nonlinear Partial Differential Equation ◽  
Variational Iteration Method ◽  
Inhomogeneous Media ◽  
Nonlinear Boltzmann Equation ◽  
Variational Iteration

The time-dependent nonlinear Boltzmann equation, which describes the time evolution of a single-particle distribution in a dilute gas of particles interacting only through binary collisions, is considered for spatially homogeneous and inhomogeneous media without external force and energy source. The nonlinear Boltzmann equation is converted to a nonlinear partial differential equation for the generating function of the moments of the distribution function. The variational-iteration method derived by He is used to solve the nonlinear differential equation of the generating function. The moments for both homogeneous and inhomogeneous media are calculated and represented graphically as functions of space and time. The distribution function is calculated from its moments using the cosine Fourier transformation. The distribution functions for the homogeneous and inhomogeneous media are represented graphically as functions of position and time.

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 Variational Iteration Method for the Solution of Differential Equation of Motion of the Mathematical Pendulum and Duffing-Harmonic Oscillator

2019 ◽  
pp. 101-109
Author(s):  
Muhammad Munib Khan
Keyword(s):  
Differential Equation ◽  
Harmonic Oscillator ◽  
Lagrange Multipliers ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Equation Of Motion ◽  
Mathematical Pendulum ◽  
Variational Iteration ◽  
Common Problems

In this work, the differential equation of motion of the undamped mathematical pendulum and Duffing-harmonic oscillator are discussed by using the variational iteration method. Additionally, common problems of pendulum are classified and Lagrange multipliers are obtained for each type of problem. Examples are given for illustration.

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