Bilgisayar Bilimleri Fakültesi

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EXISTENCE OF THREE POSITIVE SOLUTIONS FOR AN m-POINT BOUNDARY-VALUE PROBLEM ON TIME SCALES
(TEXAS STATE UNIV, 601 UNIVERSTITY DRIVE, SAN MARCOS, TX 78666 USA, 2013) Dogan, Abdulkadir; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Dogan, Abdulkadir
We study an m-point boundary-value problem on times scales. By using a fixed point theorem, we prove the existence of at least three positive solutions, under suitable growth conditions imposed on the nonlinear term. An example is given to illustrate our results.
Numerical solutions of the kawahara equation by the septic B-spline collocation method
(International Academic Press, 2014) Karakoç, Battal Gazi; Zeybek, Halil; Ak, Turgut; AGÜ; Zeybek, Halil
In this article, a numerical solution of the Kawahara equation is presented by septic B-spline collocation method. Applying the Von-Neumann stability analysis, the present method is shown to be unconditionally stable. The accuracy of the proposed method is checked by two test problems. L2 and L∞ error norms and conserved quantities are given at selected times. The obtained results are found in good agreement with the some recent results.
EXISTENCE OF POSITIVE SOLUTIONS FOR p-LAPLACIAN AN m-POINT BOUNDARY VALUE PROBLEM INVOLVING THE DERIVATIVE ON TIME SCALES
(TEXAS STATE UNIV, 601 UNIVERSTITY DRIVE, SAN MARCOS, TX 78666 USA, 2014) Dogan, Abdulkadir; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Dogan, Abdulkadir
We are interested in the existence of positive solutions for the p-Laplacian dynamic equation on time scales (phi(P)(u(Delta)(t)))(V) a(t)f (t, u Delta(t), (t)) = 0, t is an element of (0,T)(T), subject to the multipoint boundary condition, u(0) = Sigma(m-2)(i=1) alpha iu, (xi(i)) = u Delta(T) = 0, where phi(p)(S) = vertical bar s vertical bar p(-2) s, p > 1, xi i is an element of [0, T](T,) 0 < xi 1 < xi 2 < . . . < xi m-2 < p(T). By using fixed point theorems, we prove the existence of at least three nonnegatvie solutions, two of them positive, to the above boundary value problem. The interesting point is the nonlinear term f is involved with the first order derivative explicitly. An example is given to illustrate the main result.
Existence of Countably Many Positive Solutions for Nonlinear Boundary Value Problems on Time Scales
(NATURAL SCIENCES PUBLISHING CORP-NSPPO BOX 32038, ISA TOWN 00000, BAHRAIN, 2014) Dogan, Abdulkadir; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Dogan
In this paper, we consider the existence of countably many positive solutions for nonlinear singular boundary value problem on time scales. By using the fixed-point index theory and a new fixed-point theorem in cones, the sufficient conditions for the existence of countably many positive solutions are established.
ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR THE ONE-DIMENSIONAL p-LAPLACIAN BOUNDARY VALUE PROBLEMS ON TIME SCALES
(DYNAMIC PUBLISHERS, INC, 2015) Dogan, Abdulkadir; AGÜ; Dogan, Abdulkadir
In this paper, we study the following p-Laplacian boundary value problems on time scales {(phi(p)(u(Delta)(t)))(del) + a(t)f(t, u(t), u(Delta)(t)) = 0, t is an element of [0,T](T), u(0) - B-0(u(Delta)(0)) = 0, u(Delta)(T) = 0, where phi(p)(u) = vertical bar u vertical bar(p-2)u, for p > 1. We prove the existence of triple positive solutions for the one-dimensional p-Laplacian boundary value problem by using the Leggett-Williams fixed point theorem. The interesting point in this paper is that the non-linear term f is involved with first-order derivative explicitly. An example is also given to illustrate the main result.
TRIPLE POSITIVE SOLUTIONS FOR m-POINT BOUNDARY-VALUE PROBLEMS OF DYNAMIC EQUATIONS ON TIME SCALES WITH p-LAPLACIAN
(TEXAS STATE UNIV, 601 UNIVERSTITY DRIVE, SAN MARCOS, TX 78666 USA, 2015) Dogan, Abdulkadir; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Dogan, Abdulkadir
In this article we study the existence of positive solutions for m-point dynamic equation on time scales with p-Laplacian. We prove that the boundary-value problem has at least three positive solutions by applying the five functionals fixed-point theorem. An example demonstrates the main results.
THE EXISTENCE OF POSITIVE SOLUTIONS FOR A SEMIPOSITONE SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEM
(DYNAMIC PUBLISHERS, INC, 2015) Dogan, Abdulkadir; AGÜ; Dogan, Abdulkadir
In this paper, we study the existence of positive solutions to boundary value problem {u '' + lambda f(t,u)=0, t is an element of(0,1); u(0)=Sigma(m-2)(i-1) alpha (i)u(xi(i)), u'(1) = Sigma (m-2)(i=1) beta(i) u'(xi(i)), where xi(i) is an element of(0, 1), 0 < xi(1) < xi(2) < ... < xi(m-2) < 1, alpha(i), beta(i) is an element of[0,infinity), lambda is positive parameter. By using Krasnoserskii's fixed point theorem, we provide sufficient conditions for the existence of at least one positive solution to the above boundary value problem.
On the existence of positive solutions for the second-order boundary value problem
(PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND, 2015) Dogan, Abdulkadir; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Dogan, Abdulkadir
This paper is concerned with the existence of positive solutions to a second order boundary value problem. By imposing growth conditions on f and using a generalization of the Leggett-Williams fixed point theorem, we prove the existence of at least three symmetric positive solutions. (C) 2015 Elsevier Ltd. All rights reserved.
A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline
(Springer, 2016) Zeybek, Halil; Karakoç, Battal Gazi; AGÜ; Zeybek, Halil
In this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms [Formula: see text] and [Formula: see text] and the conservative quantities [Formula: see text], [Formula: see text] and [Formula: see text] are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.
Multiple positive solutions of nonlinear m-point dynamic equations for p-Laplacian on time scales
(SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAK, ATATURK BULVARI NO 221, KAVAKLIDERE, TR-06100 ANKARA, TURKEY, 2016) Dogan, Abdulkadir; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Dogan, Abdulkadir
In this paper, we study the existence of positive solutions of a nonlinear m-point p-Laplacian dynamic equation (phi(p) (x(Delta)(t)))(del) w(t)f (t,x(t), x(Delta)(t)) = 0, t(1) < m-1 X(ti) - B-0 (Sigma m-1 i=2 a(i)x(Delta)(t(i))) = 0, x(Delta) (tm) = 0, or x(Delta)(t(1)) - 0, x(t(m)) + B-1(Sigma m-1 i=2 b(i)s(Delta)(t(i))) -0, where phi(p)(s) =vertical bar s vertical bar(P-2) s, p > 1. Sufficient conditions for the existence of at least three positive solutions of the problem are obtained by using a fixed point theorem. The interesting point is the nonlinear term f is involved with the first order derivative explicitly. As an application, an example is given to illustrate the result.
A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation
(International Academic Press, 2016) Battal Gazi Karakoç S.; Zeybek, Halil; AGÜ; Zeybek, Halil
The generalized equal width (GEW) wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods.
A septic B-spline collocation method for solving the generalized equal width wave equation
(ACADEMIC PUBLICATION COUNCIL, 2016) Karakoc, Seydi B. G.; Zeybek, Halil; AGÜ; Zeybek, Halil
In this work, a septic B-spline collocation method is implemented to find the numerical solution of the generalized equal width (GEW) wave equation by using two different linearization techniques. Test problems including single soliton, interaction of solitons and Maxwellian initial condition are solved to verify the proposed method by calculating the error norms L2 and L∞ and the invariants I1, I2 and I3. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. As a result, the obtained results are found in good agreement with the some recent results.
Eigenvalue problems for nonlinear third-order m-point p-Laplacian dynamic equations on time scales
(WILEY111 RIVER ST, HOBOKEN 07030-5774, NJ, 2016) Dogan, Abdulkadir; 0000-0002-7532-1920; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Dogan, Abdulkadir
This work deals with the existence and uniqueness of a nontrivial solution for the third-order p-Laplacian m-point eigenvalue problems on time scales. We find several sufficient conditions of the existence and uniqueness of nontrivial solution of eigenvalue problems when lambda is in some interval. The proofs are based on the nonlinear alternative of Leray-Schauder. To illustrate the results, some examples are included. Copyright (C) 2014 John Wiley & Sons, Ltd.
Solitary-wave solutions of the GRLW equation using septic B-spline collocation method
(ELSEVIER SCIENCE INC, 2016) Karakoc, Seydi; Zeybek, Halil; AGÜ; Zeybek, Halil
In this work, solitary-wave solutions of the generalized regularized long wave (GRLW) equation are obtained by using septic B-spline collocation method with two different linearization techniques. To demonstrate the accuracy and efficiency of the numerical scheme, three test problems are studied by calculating the error norms L2 and L∞ and the invariants I1, I2 and I3. A linear stability analysis based on the von Neumann method of the numerical scheme is also investigated. Consequently, our findings indicate that our numerical scheme is preferable to some recent numerical schemes.
A NEW APPROACH FOR NUMERICAL SOLUTION OF LINEAR AND NON-LINEAR SYSTEMS
(KOREAN SOC COMPUTATIONAL & APPLIED MATHEMATICS & KOREAN SIGCAM, 2017) Zeybek, Halil; Dolapci, Ihsan Timucin; AGÜ; Zeybek, Halil
In this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.
On the existence of positive solutions of the p-Laplacian dynamic equations on time scales
(WILEY, 2017) DOĞAN, Abdülkadir; 0000-0002-7532-1920; AGÜ; DOĞAN, Abdülkadir
In this paper, we investigate the existence of positive solutions for a nonlinear m-point boundary value problem for the p-Laplacian dynamic equations on time scales, by applying a Krasnosel'skii's fixed point theorem. As an application, an example is included to demonstrate themain results.
EIGENVALUE PROBLEMS FOR SINGULAR MULTI-POINT DYNAMIC EQUATIONS ON TIME SCALES
(TEXAS STATE UNIV, 601 UNIVERSTITY DRIVE, SAN MARCOS, TX 78666 USA, 2017) Dogan, Abdulkadir; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Dogan, Abdulkadir
In this article, we study a singular multi-point dynamic eigenvalue problem on time scales. We find existence of positive solutions by constructing the Green's function and studying its positivity eigenvalue intervals. Two examples are given to illustrate our results.
APPLICATION OF THE COLLOCATION METHOD WITH B-SPLINES TO THE GEW EQUATION
(KENT STATE UNIVERSITYETNA, DEPT MATHEMATICS & COMPUTER SCIENCE, KENT, OH 44242-0001, 2017) Zeybek, Halil; Karakoc, S. Battal Gazi; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
In this paper, the generalized equal width (GEW) wave equation is solved numerically by using a quintic B-spline collocation algorithm with two different linearization techniques. Also, a linear stability analysis of the numerical scheme based on the von Neumann method is investigated. The numerical algorithm is applied to three test problems consisting of a single solitary wave, the interaction of two solitary waves, and a Maxwellian initial condition. In order to determine the performance of the numerical method, we compute the error in the L-2- and L-infinity- norms and in the invariants I-1, I-2, and I-3 of the GEW equation. These calculations are compared with earlier studies. Afterwards, the motion of solitary waves according to different parameters is designed.
On the existence of positive solutions of the p-Laplacian dynamic equations on time scales
(WILEY111 RIVER ST, HOBOKEN 07030-5774, NJ, 2017) Dogan, Abdulkadir; 0000-0002-7532-1920; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
In this paper, we investigate the existence of positive solutions for a nonlinear m-point boundary value problem for the p-Laplacian dynamic equations on time scales, by applying a Krasnosel'skii's fixed point theorem. As an application, an example is included to demonstrate themain results. Copyright (C) 2017 John Wiley & Sons, Ltd.
A New Semi-supervised Classification Method Based on Mixture Model Clustering for Classification of Multispectral Data
(SPRINGER, 233 SPRING ST, NEW YORK, NY 10013 USA, 2018) Gogebakan, Maruf; Erol, Hamza; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü
A new method for semi-supervised classification of remotely-sensed multispectral image data is developed in this study. It consists of unsupervised-clustering for data labelling and supervised-classification of clusters in multispectral image data (MID) using spectral signatures. Mixture model clustering, based on model selection, is proposed for finding the number and determining the structures of clusters in MID. The best mixture model, for the best clustering of data, finds the number and determines the structure of clusters in MID. The number of elements in the best mixture model fits to the number of clusters in MID. The elements of the best mixture model fits to the structure of clusters in MID. Clusters in MID is supervised-classified using spectral signatures. Euclidean distance is used as the discrimination function for the supervised-classification method. The values of Euclidean distances are used as decision rule for the supervised-classification method.

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