The Sturm-Liouville operator on the space of functions with discontinuity conditions

Date

2006-03-01

Author

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

247
views

0
downloads

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.

Subject Keywords

Impulsive differential equation, Boundary value problem, Sturm-Liouville problem, Eigenvalue problem

URI

https://hdl.handle.net/11511/31927

Journal

COMPUTERS & MATHEMATICS WITH APPLICATIONS

DOI

https://doi.org/10.1016/j.camwa.2005.11.034

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

An eigenfunction expansion for the Schrodinger equation with arbitrary non-central potentials Taşeli, Hasan; Uğur, Ömür (2002-11-01) An eigenfunction expansion for the Schrodinger equation for a particle moving in an arbitrary non-central potential in the cylindrical polar coordinates is introduced, which reduces the partial differential equation to a system of coupled differential equations in the radial variable r. It is proved that such an orthogonal expansion of the wavefunction into the complete set of Chebyshev polynomials is uniformly convergent on any domain of (r, theta). As a benchmark application, the bound states calculations...
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...
An Asymptotic-Numerical Hybrid Method for Solving Singularly Perturbed Linear Delay Differential Equations Cengizci, Süleyman (Hindawi Limited, 2017) In thiswork, approximations to the solutions of singularly perturbed second-order linear delay differential equations are studied. We firstly use two-term Taylor series expansion for the delayed convection term and obtain a singularly perturbed ordinary differential equation (ODE). Later, an efficient and simple asymptotic method so called Successive Complementary Expansion Method (SCEM) is employed to obtain a uniformly valid approximation to this corresponding singularly perturbed ODE. As the final step, ...
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...
Variational iteration method for Sturm-Liouville differential equations ALTINTAN, DERYA; Uğur, Ömür (2009-07-01) 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...

Citation Formats

Ö. Uğur, “The Sturm-Liouville operator on the space of functions with discontinuity conditions,” COMPUTERS & MATHEMATICS WITH APPLICATIONS, pp. 889–896, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31927.