Variational iteration method for solving nonlinear boundary value problems

Momani, Shaher; Abuasad, Salah; Odibat, Zaid

doi:10.1016/j.amc.2006.05.138

Cited by 76 publications

(45 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper applies the variational iteration method to the discussed problems. The variational iteration method was developed by Ji-Huan He [1,2,3,4,5] and is useful for solving a wide range of problems [1,2,3,7,5,8,9,4,6,10,11]. The application of the variational iteration method for direct and inverse Stefan problems with a Dirichlet boundary condition is considered in paper [12].…”

Section: Introductionmentioning

confidence: 99%

Application of the Variational Iteration Method for Inverse Stefan Problem with Neumann’s Boundary Condition

Słota

2008

Computational Science – ICCS 2008

View full text Add to dashboard Cite

Abstract. In this paper, the possibility of application of the variational iteration method for solving the inverse Stefan problem with a Neumann boundary condition is presented. This problem consists in a calculation of temperature distribution as well as in the reconstruction of the function which describes the heat flux on the boundary, when the position of the moving interface is known. The validity of the approach is verified by comparing the results obtained with the analytical solution.

show abstract

Section: Introductionmentioning

confidence: 99%

Application of the Variational Iteration Method for Inverse Stefan Problem with Neumann’s Boundary Condition

Słota

2008

Computational Science – ICCS 2008

View full text Add to dashboard Cite

show abstract

“…The method gives rapidly convergent successive approximations of the exact solution if such a solution exists; otherwise a few approximations can be used for numerical purposes. The VIM was successfully applied to autonomous ordinary and partial differential equations [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Recently in [15] the VIM has been implemented for finding the solution of differentialalgebraic equations.…”

Section: Introductionmentioning

confidence: 99%

Application of Chebyshev Approximation in the Process of Variational Iteration Method for Solving Differentialalgebraic Equations

Ghovatmand

Hosseini

Nilli

2011

MCA

View full text Add to dashboard Cite

Abstract-In this paper, we use Chebyshev approximations in the process of He's variational iteration method for finding the solution of differential-algebraic equations. This allows us to make integration at each of the iterations possible and at the same time, obtain a good accuracy in a reasonable number of iterations. Numerical results show that using Chebyshev approximation is much more efficient than using Taylor approximation which is more popular.First, an index reduction technique is implemented for semi-explicit differentialalgebraic equations, then the obtained problem is solved by He's variational iteration method. The scheme is tested for some high index differential-algebraic equations and the results demonstrate reliability and efficiency of the proposed method.

show abstract

“…The given solution is considered as the fixed point of the following functional [11] under the suitable choice of initial approximation [21] u 0 ðxÞ at n ¼ 0. We use finite element method to determine the starting function to avoid the arbitrary choice of starting function.…”

Section: Introductionmentioning

confidence: 99%

On the solutions of three-point boundary value problems using variational-fixed point iteration method

Kılıçman

Wadai

2016

Math Sci

View full text Add to dashboard Cite

Given a three-point fourth-order boundary value problems y ðivÞ þ pðxÞy 000 þ qðxÞy 00 þ rðxÞy 0 þ sðxÞy ¼ f ðxÞ; a x b such that yðaÞ ¼ yðbÞ ¼ y 00 ðbÞ ¼ y 00 ðaÞ ¼ 0; a a b; where p; q; r; s; f 2 C½a; b , we combine the application of variational iteration method and fixed point iteration process to construct an iterative scheme called variationalfixed point iteration method that approximates the solution of three-point boundary value problems. The success of the variational or weighted residual method of approximation from a practical point of view depends on the suitable selection of the basis function. The method is self correcting one and leads to fast convergence. Problems were experimented to show the effectiveness and accuracy of the proposed method.Keywords Fixed point iteration Á Variational iteration method Á Lagrange's multiplier and boundary value problems.

show abstract

Variational iteration method for solving nonlinear boundary value problems

Cited by 76 publications

References 23 publications

Application of the Variational Iteration Method for Inverse Stefan Problem with Neumann’s Boundary Condition

Application of the Variational Iteration Method for Inverse Stefan Problem with Neumann’s Boundary Condition

Application of Chebyshev Approximation in the Process of Variational Iteration Method for Solving Differentialalgebraic Equations

On the solutions of three-point boundary value problems using variational-fixed point iteration method

Contact Info

Product

Resources

About