Ozgur Yildirim - Academia.edu (original) (raw)

Papers by Ozgur Yildirim

Nucleation and Atmospheric Aerosols, 2016

In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with N... more In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with Neumann conditions is considered. Third and fourth order of accuracy stable difference schemes for solving this problem are presented. Efficiency of these schemes are tested via MATLAB implementation.

Nonlinear Analysis-Modelling and Control, Nov 1, 2020

In this paper, we study the existence and uniqueness of weak solution for the system of finite di... more In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability. We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

Nucleation and Atmospheric Aerosols, 2018

In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications i... more In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications in physics and biology is considered. A special case of this system, which describe the open states in DNA double helices is studied. Numerical solution of this system is obtained by finite difference method with fixed point iteration. Some examples are considered and the results of numerical experiments are presented.In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications in physics and biology is considered. A special case of this system, which describe the open states in DNA double helices is studied. Numerical solution of this system is obtained by finite difference method with fixed point iteration. Some examples are considered and the results of numerical experiments are presented.

Discrete Dynamics in Nature and Society, 2015

This paper presents a third order of accuracy stable difference scheme for the approximate soluti... more This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

Numerical Functional Analysis and Optimization, Apr 10, 2017

This paper presents a fourth order of accuracy unconditionally stable difference scheme for the a... more This paper presents a fourth order of accuracy unconditionally stable difference scheme for the approximate solution of multipoint nonlocal boundary value hyperbolic problem in a Hilbert space with a self-adjoint positive definite operator. Stability estimates for the solution of this difference scheme are established. In order to support the theoretical statements some results of numerical experiments are presented using finite difference method.

Nucleation and Atmospheric Aerosols, 2019

This study presents the numerical solution of coupled Klein-Gordon equations, which models exchan... more This study presents the numerical solution of coupled Klein-Gordon equations, which models exchange of energy between two different components of one-dimensional nonlinear wave process. A composite numerical method based on the first order of accuracy finite different scheme and fixed point iteration is implemented to solve coupled Klein-Gordon equations with appropriate initial and boundary conditions. A test problem is employed and results of numerical experiments are presented with error analysis.

Applied Mathematics and Computation, Mar 1, 2015

In this article, we consider third and fourth order of accuracy stable difference schemes for the... more In this article, we consider third and fourth order of accuracy stable difference schemes for the approximate solutions of hyperbolic multipoint nonlocal boundary value problem in a Hilbert space H with self-adjoint positive definite operator A. We present stability estimates and numerical analysis for the solutions of the difference schemes using finite difference method.

Springer Proceedings in Mathematics & Statistics, 2021

THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019), 2019

This study presents the numerical solution of coupled Klein-Gordon equations, which models exchan... more This study presents the numerical solution of coupled Klein-Gordon equations, which models exchange of energy between two different components of one-dimensional nonlinear wave process. A composite numerical method based on the first order of accuracy finite different scheme and fixed point iteration is implemented to solve coupled Klein-Gordon equations with appropriate initial and boundary conditions. A test problem is employed and results of numerical experiments are presented with error analysis.

AIP Conference Proceedings, 2018

In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications i... more In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications in physics and biology is considered. A special case of this system, which describe the open states in DNA double helices is studied. Numerical solution of this system is obtained by finite difference method with fixed point iteration. Some examples are considered and the results of numerical experiments are presented.In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications in physics and biology is considered. A special case of this system, which describe the open states in DNA double helices is studied. Numerical solution of this system is obtained by finite difference method with fixed point iteration. Some examples are considered and the results of numerical experiments are presented.

Numerical Functional Analysis and Optimization, 2017

This paper presents a fourth order of accuracy unconditionally stable difference scheme for the a... more This paper presents a fourth order of accuracy unconditionally stable difference scheme for the approximate solution of multipoint nonlocal boundary value hyperbolic problem in a Hilbert space with a self-adjoint positive definite operator. Stability estimates for the solution of this difference scheme are established. In order to support the theoretical statements some results of numerical experiments are presented using finite difference method.

AIP Conference Proceedings, 2016

In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with N... more In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with Neumann conditions is considered. Third and fourth order of accuracy stable difference schemes for solving this problem are presented. Efficiency of these schemes are tested via MATLAB implementation.

Discrete Dynamics in Nature and Society, 2015

This paper presents a third order of accuracy stable difference scheme for the approximate soluti... more This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

Applied Mathematics and Computation, 2015

In this article, we consider third and fourth order of accuracy stable difference schemes for the... more In this article, we consider third and fourth order of accuracy stable difference schemes for the approximate solutions of hyperbolic multipoint nonlocal boundary value problem in a Hilbert space H with self-adjoint positive definite operator A. We present stability estimates and numerical analysis for the solutions of the difference schemes using finite difference method.

Nonlinear Analysis: Modelling and Control, 2020

In this paper, we study the existence and uniqueness of weak solution for the system of finite di... more In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

Nucleation and Atmospheric Aerosols, 2012

ABSTRACT The abstract nonlocal boundary value problem for the hyperbolic equation {u '&am... more ABSTRACT The abstract nonlocal boundary value problem for the hyperbolic equation {u '' (t) + Au(t) = f (t), 0 < t < T, u(0) = alpha u(1) + phi, u'(0) = beta u'(1) + psi in a Hilbert space H with the self - adjoint positive definite operator A is considered. The third and fourth order of accuracy difference schemes for the approximate solutions of this problem are presented. The stability estimates for the solutions of these difference schemes are obtained and numerical results are presented in order to verify theoretical statements.

Nucleation and Atmospheric Aerosols, 2011

In the present paper, two new second order of accuracy absolutely stable difference schemes are p... more In the present paper, two new second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value problemd2u(t)dt2+Au(t) = f(t) (0<=t<=1),u(0) = j = 1nalphaju(lambdaj)+J,ut(0) = j = 1nbetajut(lambdaj)+psi,0<lambda1<lambda2<...<lambdan<=1 for differential equations in a Hilbert space H with the self-adjoint positive definite operator A. The stability estimates for the solutions of these difference schemes are established.

Boundary Value Problems, Feb 15, 2013

The abstract Cauchy problem for the hyperbolic equation in a Hilbert space H with self-adjoint po... more The abstract Cauchy problem for the hyperbolic equation in a Hilbert space H with self-adjoint positive definite operator A is considered. The third and fourth orders of accuracy difference schemes for the approximate solution of this problem are presented. The stability estimates for the solutions of these difference schemes are established. A finite difference method and some results of numerical experiments are presented in order to support theoretical statements.

Nucleation and Atmospheric Aerosols, 2016

In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with N... more In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with Neumann conditions is considered. Third and fourth order of accuracy stable difference schemes for solving this problem are presented. Efficiency of these schemes are tested via MATLAB implementation.

Nonlinear Analysis-Modelling and Control, Nov 1, 2020

In this paper, we study the existence and uniqueness of weak solution for the system of finite di... more In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability. We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

Nucleation and Atmospheric Aerosols, 2018

In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications i... more In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications in physics and biology is considered. A special case of this system, which describe the open states in DNA double helices is studied. Numerical solution of this system is obtained by finite difference method with fixed point iteration. Some examples are considered and the results of numerical experiments are presented.In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications in physics and biology is considered. A special case of this system, which describe the open states in DNA double helices is studied. Numerical solution of this system is obtained by finite difference method with fixed point iteration. Some examples are considered and the results of numerical experiments are presented.

Discrete Dynamics in Nature and Society, 2015

This paper presents a third order of accuracy stable difference scheme for the approximate soluti... more This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

Numerical Functional Analysis and Optimization, Apr 10, 2017

This paper presents a fourth order of accuracy unconditionally stable difference scheme for the a... more This paper presents a fourth order of accuracy unconditionally stable difference scheme for the approximate solution of multipoint nonlocal boundary value hyperbolic problem in a Hilbert space with a self-adjoint positive definite operator. Stability estimates for the solution of this difference scheme are established. In order to support the theoretical statements some results of numerical experiments are presented using finite difference method.

Nucleation and Atmospheric Aerosols, 2019

This study presents the numerical solution of coupled Klein-Gordon equations, which models exchan... more This study presents the numerical solution of coupled Klein-Gordon equations, which models exchange of energy between two different components of one-dimensional nonlinear wave process. A composite numerical method based on the first order of accuracy finite different scheme and fixed point iteration is implemented to solve coupled Klein-Gordon equations with appropriate initial and boundary conditions. A test problem is employed and results of numerical experiments are presented with error analysis.

Applied Mathematics and Computation, Mar 1, 2015

In this article, we consider third and fourth order of accuracy stable difference schemes for the... more In this article, we consider third and fourth order of accuracy stable difference schemes for the approximate solutions of hyperbolic multipoint nonlocal boundary value problem in a Hilbert space H with self-adjoint positive definite operator A. We present stability estimates and numerical analysis for the solutions of the difference schemes using finite difference method.

Springer Proceedings in Mathematics & Statistics, 2021

THIRD INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2019), 2019

This study presents the numerical solution of coupled Klein-Gordon equations, which models exchan... more This study presents the numerical solution of coupled Klein-Gordon equations, which models exchange of energy between two different components of one-dimensional nonlinear wave process. A composite numerical method based on the first order of accuracy finite different scheme and fixed point iteration is implemented to solve coupled Klein-Gordon equations with appropriate initial and boundary conditions. A test problem is employed and results of numerical experiments are presented with error analysis.

AIP Conference Proceedings, 2018

In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications i... more In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications in physics and biology is considered. A special case of this system, which describe the open states in DNA double helices is studied. Numerical solution of this system is obtained by finite difference method with fixed point iteration. Some examples are considered and the results of numerical experiments are presented.In this paper, a system of nonlinear coupled sine-Gordon, which have some powerful applications in physics and biology is considered. A special case of this system, which describe the open states in DNA double helices is studied. Numerical solution of this system is obtained by finite difference method with fixed point iteration. Some examples are considered and the results of numerical experiments are presented.

Numerical Functional Analysis and Optimization, 2017

This paper presents a fourth order of accuracy unconditionally stable difference scheme for the a... more This paper presents a fourth order of accuracy unconditionally stable difference scheme for the approximate solution of multipoint nonlocal boundary value hyperbolic problem in a Hilbert space with a self-adjoint positive definite operator. Stability estimates for the solution of this difference scheme are established. In order to support the theoretical statements some results of numerical experiments are presented using finite difference method.

AIP Conference Proceedings, 2016

In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with N... more In this work, a multipoint nonlocal boundary value problem (NBVP) for hyperbolic equations with Neumann conditions is considered. Third and fourth order of accuracy stable difference schemes for solving this problem are presented. Efficiency of these schemes are tested via MATLAB implementation.

Discrete Dynamics in Nature and Society, 2015

This paper presents a third order of accuracy stable difference scheme for the approximate soluti... more This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

Applied Mathematics and Computation, 2015

In this article, we consider third and fourth order of accuracy stable difference schemes for the... more In this article, we consider third and fourth order of accuracy stable difference schemes for the approximate solutions of hyperbolic multipoint nonlocal boundary value problem in a Hilbert space H with self-adjoint positive definite operator A. We present stability estimates and numerical analysis for the solutions of the difference schemes using finite difference method.

Nonlinear Analysis: Modelling and Control, 2020

In this paper, we study the existence and uniqueness of weak solution for the system of finite di... more In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

Nucleation and Atmospheric Aerosols, 2012

ABSTRACT The abstract nonlocal boundary value problem for the hyperbolic equation {u '&am... more ABSTRACT The abstract nonlocal boundary value problem for the hyperbolic equation {u '' (t) + Au(t) = f (t), 0 < t < T, u(0) = alpha u(1) + phi, u'(0) = beta u'(1) + psi in a Hilbert space H with the self - adjoint positive definite operator A is considered. The third and fourth order of accuracy difference schemes for the approximate solutions of this problem are presented. The stability estimates for the solutions of these difference schemes are obtained and numerical results are presented in order to verify theoretical statements.

Nucleation and Atmospheric Aerosols, 2011

In the present paper, two new second order of accuracy absolutely stable difference schemes are p... more In the present paper, two new second order of accuracy absolutely stable difference schemes are presented for the nonlocal boundary value problemd2u(t)dt2+Au(t) = f(t) (0<=t<=1),u(0) = j = 1nalphaju(lambdaj)+J,ut(0) = j = 1nbetajut(lambdaj)+psi,0<lambda1<lambda2<...<lambdan<=1 for differential equations in a Hilbert space H with the self-adjoint positive definite operator A. The stability estimates for the solutions of these difference schemes are established.

Boundary Value Problems, Feb 15, 2013

The abstract Cauchy problem for the hyperbolic equation in a Hilbert space H with self-adjoint po... more The abstract Cauchy problem for the hyperbolic equation in a Hilbert space H with self-adjoint positive definite operator A is considered. The third and fourth orders of accuracy difference schemes for the approximate solution of this problem are presented. The stability estimates for the solutions of these difference schemes are established. A finite difference method and some results of numerical experiments are presented in order to support theoretical statements.