Bilgisayar Bilimleri Fakültesi/Faculty of Computer Sciences

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/45

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Positive solutions of multipoint φ-Laplacian BVPs with first-order derivative dependence
(World Scientific, 2023) Bachouche K.; Tair H.; DOĞAN, Abdülkadir; 0000-0002-3195-4718 View this author’s ORCID profile; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Doğan, Abdülkadir
This paper concerns existence of positive solutions for a second-order boundary value problem of Sturm-Liouville type associated with a φ-Laplacian operator and posed on a bounded interval. Existence results are obtained by an adapted version of the Krasnosel'skii's fixed point theorem of cone expansion and compression. Some examples 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.
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.
Normal Mixture Model-Based Clustering of Data Using Genetic Algorithm
(SPRINGER INTERNATIONAL PUBLISHING AG, 2020) Gogebakan, Maruf; Erol, Hamza; AGÜ; Gogebakan, Maruf
In this study, a new algorithm was developed for clustering multivariate big data. Normal mixture distributions are used to determine the partitions of variables. Normal mixture models obtained from the partitions of variables are generated using Genetic Algorithms (GA). Each partition in the variables corresponds to a clustering center in the normal mixture model. The best model that fits the data structure from normal mixture models is obtained by using the information criteria obtained from normal mixture distributions.
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.
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.
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 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.
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 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.
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.
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.
Comparative assessment of smooth and non-smooth optimization solvers in HANSO software
(Balikesir University, 2022) Tor, Ali Hakan; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü; Tor, Ali Hakan
The aim of this study is to compare the performance of smooth and nonsmooth optimization solvers from HANSO (Hybrid Algorithm for Nonsmooth Optimization) software. The smooth optimization solver is the implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and the nonsmooth optimization solver is the Hybrid Algorithm for Nonsmooth Optimization. More precisely, the nonsmooth optimization algorithm is the combination of the BFGS and the Gradient Sampling Algorithm (GSA). We use well-known collection of academic test problems for nonsmooth optimization containing both convex and nonconvex problems. The motivation for this research is the importance of the comparative assessment of smooth optimization methods for solving nonsmooth optimization problems. This assessment will demonstrate how successful is the BFGS method for solving nonsmooth optimization problems in comparison with the nonsmooth optimization solver from HANSO. Performance profiles using the number iterations, the number of function evaluations and the number of subgradient evaluations are used to compare solvers. © 2021 Balikesir University. All rights reserved.
A Modified Multiple Shooting Algorithm for Parameter Estimation in ODEs Using Adjoint Sensitivity Analysis
(ELSEVIER SCIENCE INCSTE 800, 230 PARK AVE, NEW YORK, NY 10169, 2021) Aydogmus, Ozgur; Tor, Ali Hakan; 0000-0003-3193-5004; 0000-0002-9463-7197; AGÜ, Bilgisayar Bilimleri Fakültesi, Bilgisayar Bilimleri Fakültesi/Faculty of Computer Sciences
To increase the predictive power of a model, one needs to estimate its unknown parameters. Almost all parameter estimation techniques in ordinary differential equation models suffer from either a small convergence region or enormous computational cost. The method of multiple shooting, on the other hand, takes its place in between these two extremes. The computational cost of the algorithm is mostly due to the calculation of directional derivatives of objective and constraint functions. Here we modify the multiple shooting algorithm to use the adjoint method in calculating these derivatives. In the literature, this method is known to be a more stable and computationally efficient way of computing gradients of scalar functions. A predator-prey system is used to show the performance of the method and supply all necessary information for a successful and efficient implementation. (C) 2020 Elsevier Inc. All rights reserved.
Existence results for a class of boundary value problems for fractional differential equations
(SCIENTIFIC TECHNICAL RESEARCH COUNCIL TURKEY-TUBITAKATATURK BULVARI NO 221, KAVAKLIDERE, TR-06100 ANKARA, TURKEY, 2021) Dogan, Abdulkadir; AGÜ, Mühendislik Fakültesi, Bilgisayar Mühendisliği Bölümü; Dogan, Abdulkadir
By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the LeraySchauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).
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.
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.
On the Existence of Positive Solutions for the Time-Scale Dynamic Equations on Infinite Intervals
(Springer, 2020) Dogan A.; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü
This paper investigates the existence of positive solutions to time-scale boundary value problems on infinite intervals. By applying the Leggett-Williams fixed point theorem in a cone, some new results for the existence of at least three positive solutions of boundary value problems are found. With infinite intervals, the theorem can be used to prove the existence of solutions of boundary value problems for nonlinear dynamic equations dependence on the delta derivative explicitly. Our results are new for the special cases of difference equations and differential equations as well as in the general time scale setting.
ROI Detection in Mammogram Images using Wavelet-Based Haralick and HOG Features
(IEEE, 345 E 47TH ST, NEW YORK, NY 10017 USA, 2018) Tasdemir, Sena Busra Yengec; Tasdemir, Kasim; Aydin, Zafer; 0000-0003-4542-2728; AGÜ, Mühendislik Fakültesi, Mühendislik Bilimleri Bölümü
Digital mammography is a widespread medical imaging technique that is used for early detection and diagnosis of breast cancer. Detecting the region of interest (ROI) helps to locate the abnormal areas, which may be analyzed further by a radiologist or a CAD system. In this paper, a new classification method is proposed for ROI detection in mammography images. Features are extracted using Wavelet transform, Haralick and HOG descriptors. To reduce the number of dimensions and eliminate irrelevant features, a wrapper-based feature selection method is implemented. Several feature extraction methods and machine learning classifiers are compared by performing a leave-one-image-out cross-validation experiment on a difficult dataset. The proposed feature extraction method provides the best accuracy of 87.5% and the second-best area under curve (AUC) score of 84% when employed in a random forest classifier.

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