Variational iteration method for Sturm-Liouville differential equations

Date

2009-07-01

Author

ALTINTAN, DERYA
Uğur, Ömür

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

203
views

0
downloads

In this article, He's variational iteration method is applied to linear Sturm-Liouville eigenvalue and boundary value problems, including the harmonic oscillator. In this method, solutions of the problems are approximated by a set of functions that may include possible constants to be determined from the boundary conditions. By computing variations, the Lagrange multipliers are derived and the generalised expressions of variational iterations are constructed. Numerical results show that the method is simple, however powerful and effective.

Subject Keywords

Variational iteration method, Sturm-Liouville equations, Eigenvalue problems, Boundary value problems, Computing variations, Lagrange multipliers

URI

https://hdl.handle.net/11511/29958

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS

DOI

https://doi.org/10.1016/j.camwa.2009.02.029

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Solution of initial and boundary value problems by the variational iteration method Altintan, D.; Uğur, Ömür (2014-03-15) The Variational Iteration Method (VIM) is an iterative method that obtains the approximate solution of differential equations. In this paper, it is proven that whenever the initial approximation satisfies the initial conditions, vim obtains the solution of Initial Value Problems (IVPs) with a single iteration. By using this fact, we propose a new algorithm for Boundary Value Problems (BVPs): linear and nonlinear ones. Main advantage of the present method is that it does not use Green's function, however, it...
The Sturm-Liouville operator on the space of functions with discontinuity conditions Uğur, Ömür (2006-03-01) The Sturm-Liouville differential operators defined on the space of discontinuous functions, where the moments of discontinuity of the functions are interior points of the interval and the discontinuity conditions are linear have been studied. Auxiliary results concerning the Green's formula, boundary value, and eigenvalue problems for impulsive differential equations are emphasized.
A Rayleigh–Ritz Method for Numerical Solutions of Linear Fredholm Integral Equations of the Second Kind Kaya, Ruşen; Taşeli, Hasan (2022-01-01) A Rayleigh–Ritz Method is suggested for solving linear Fredholm integral equations of the second kind numerically in a desired accuracy. To test the performance of the present approach, the classical one-dimensional Schrödinger equation -y″(x)+v(x)y(x)=λy(x),x∈(-∞,∞) has been converted into an integral equation. For a regular problem, the unbounded interval is truncated to x∈ [ - ℓ, ℓ] , where ℓ is regarded as a boundary parameter. Then, the resulting integral equation has been solved and the results are co...
Boundary value problems for higher order linear impulsive differential equations Uğur, Ömür; Akhmet, Marat (2006-07-01) In this paper higher order linear impulsive differential equations with fixed moments of impulses subject to linear boundary conditions are studied. Green's formula is defined for piecewise differentiable functions. Properties of Green's functions for higher order impulsive boundary value problems are introduced. An appropriate example of the Green's function for a boundary value problem is provided. Furthermore, eigenvalue problems and basic properties of eigensolutions are considered. (c) 2006 Elsevier In...
FINITE DIFFERENCE APPROXIMATIONS OF VARIOUS STEKLOV EIGENVALUE PROBLEMS ÖZALP, MÜCAHİT; Bozkaya, Canan; Türk, Önder; Department of Mathematics (2022-8-26) In this thesis, the finite difference method (FDM) is employed to numerically solve differently defined Steklov eigenvalue problems (EVPs) that are characterized by the existence of a spectral parameter on the whole or a part of the domain boundary. The FDM approximation of the Laplace EVP is also considered due to the fact that the defining differential operator in a Steklov EVP is the Laplace operator. The fundamentals of FDM are covered and their applications on some BVPs involving Laplace operator are d...

Citation Formats

D. ALTINTAN and Ö. Uğur, “Variational iteration method for Sturm-Liouville differential equations,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 322–328, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/29958.