Kürkçü, Ömür Kıvanç
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Kurkçu, O. K. Kurkçu, O. Kivanc Kürkçü, Ö. Kıvanç Kurkçu, Omur K. Kürkçü, Ömür K. Kurkcu, Omur Kivanc Kurkçu, Omur Kivanc Kürkcü, Ömür Kıvanç Kürkçü, Ömür Kuvanc Kürkçü, Ö. K.
Job Title
Email Address
okkurkcu@ktun.edu.tr
Main Affiliation
02.05. Department of Engineering Basic Sciences
Status
Current Staff
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Scopus Author ID
Turkish CoHE Profile ID
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WoS Researcher ID
Research Topics
Domains
Physical Sciences
Fields
MathematicsPhysics and Astronomy
Subfields
Modeling and SimulationNumerical AnalysisStatistical and Nonlinear Physics
Specific Research Areas
Fractional Differential Equations Solutions
Numerical methods for differential equations
Differential Equations and Numerical Methods
Iterative Methods for Nonlinear Equations
Nonlinear Waves and Solitons
Sustainable Development Goals
SDG data is not available
Documents
28
Citations
230
h-index
10
Documents
30
Citations
239
Publication Collaboration
| Affiliation Name | Count |
|---|---|
| Manisa Celal Bayar University | 22 |
| İzmir University of Economics | 13 |
| Konya Technical University | 13 |
| Dokuz Eylül Üniversitesi Hastanesi | 3 |
| Izmir Institute of Technology | 1 |
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Data obtained from OpenAlex
Scholarly Output
14
Articles
14
Views / Downloads
31/17
Supervised MSc Theses
0
Supervised PhD Theses
0
WoS Citation Count
42
Scopus Citation Count
49
Patents
0
Projects
0
WoS Citations per Publication
3.00
Scopus Citations per Publication
3.50
Open Access Source
2
Supervised Theses
0
| Journal | Count |
|---|---|
| Applied Numerical Mathematics | 1 |
| APPLIED NUMERICAL MATHEMATICS | 1 |
| Computational & Applied Mathematics | 1 |
| COMPUTATIONAL & APPLIED MATHEMATICS | 1 |
| Engineering computations | 1 |
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14 results
Scholarly Output Search Results
Now showing 1 - 10 of 14
Article Citation - WoS: 12Citation - Scopus: 13Pell-Lucas Series Approach for a Class of Fredholm-Type Delay Integro-Differential Equations With Variable Delays(SPRINGER HEIDELBERG, 2021-02-08) Demir, Duygu Dönmez; Lukonde, Alpha Peter; Kürkçü, Ömür Kıvanç; Sezer, Mehmet; Donmez Demir, DuyguIn this study, a Pell-Lucas matrix-collocation method is used to solve a class of Fredholm-type delay integro-differential equations with variable delays under initial conditions. The method involves the basic matrix structures gained from the expansions of the functions at collocation points. Therefore, it performs direct and immediate computation. To test its advantage on the applications, some numerical examples are evaluated. These examples show that the method enables highly accurate solutions and approximations. Besides, the accuracy of the solutions and the validity of the method are checked via the residual error analysis and the upper bound error, respectively. Finally, the numerical results, such as errors and computation time, are compared in the tables and figures.Article An Actuated Computational Method for Treating Parabolic Partial Delay Integro-Differential Equations Constrained by Infinite Boundary(Springer Basel Ag, 2023-08-21) Kurkcu, Omur KivancFor the first time via this study, the ultimate effort is inclined to numerically solve one-dimensional parabolic partial integro-differential equations with spatial-temporal delays and infinite boundary using an efficient matrix-collocation method dependent upon the orthoexponential polynomials. The method clearly actuates a novel procedure converting the unknown differential and delay terms into their matrix expansions at the collocation points, and evaluating the integral part bounded by the half-line. The existence of the singular integral part is also validated by the orthoexponential polynomial solution. In addition to these novelties, an error bound estimation is developed via a boundary property of the orthoexponential polynomials. The resulting solutions are improved via the residual error analysis. Some numerical benchmark examples are included to indicate the accuracy and validity of the method, deploying graphical and numerical instruments. It can be noticeable to conclude that the proposed method achieves both drastic and useful approximation for highly stiff problems derived from the aforementioned equations.Article Citation - WoS: 1Citation - Scopus: 1A Neural Computational Method for Solving Renewal Delay Integro-Differential Equations Constrained by the Half-Line(Springer Heidelberg, 2022-10-03) Kürkçü, Ömür KıvançThis study aims to solve the renewal delay integro-differential equations constrained by the half-line, introducing a computational method composed of the matrix relations of the Stieltjes-Wigert polynomials at the collocation points. In order to mathematically interpret their robust integral part, the method is also fed neurally by the Stieltjes-Wigert polynomials and a hybrid polynomial dependent upon the alteration of the Taylor and exponential polynomial bases. Thus, the method easily gathers the matrix relations into a matrix equation and immediately produces a desired solution. An error bound analysis is established to discuss the accuracy of the method by employing the collaboration of the mentioned polynomials. A population model with time-lags (delays), the detection of the displaced atoms versus kinetic energy, an integral delay equation, and a delayed problem with functional kernel are firstly treated by the method. Consequently, it is evident that the method presents a novel consistent approach and is directly programmable on a mathematical software thanks to its neural structure.Article Citation - WoS: 1Citation - Scopus: 1An Exclusive Spectral Computational Approach Based on Quadratic Orthoexponential Polynomials for Solving Integro-Differential Equations With Delays on the Real Line(Elsevier B.V., 2023-02-01) Kürkçü, Ömür KıvançThis study aims to bring together the ultimate formation of the integro-differential equations involving the functional delay and the singular integral with constant delay on the real line, presenting an exclusive spectral computational approach made up of quadratic orthoexponential polynomials. Frankly, the method makes possible to evaluate the singular and delayed integral part by way of the matrix expansion of quadratic property of orthoexponential polynomials, as well as transforming the unknown terms into the matrix relations. Hence, the stability of the integral part is materialized. An error improvement technique is also performed via a residual function. Several integral and integro-differential equations are considered by a devised programme, which immediately returns the method of solution. The outcomes are, thus, exposed to be compared sensitively in tables and figures. Having investigated the comparisons, one can admit that the method accomplishes exclusive and efficient approximation to the equations in question. © 2022 IMACSArticle Citation - WoS: 1Citation - Scopus: 1An Accurate and Novel Numerical Simulation With Convergence Analysis for Nonlinear Partial Differential Equations of Burgers-Fisher Type Arising in Applied Sciences(Walter De Gruyter Gmbh, 2021-02-17) Kürkçü, Ömür Kuvanc; Sezer, MehmetIn this study, the second-order nonlinear partial differential equations of Burgers-Fisher type are considered under a unique formulation by introducing a novel highly accurate numerical method based on the Norlund rational polynomial and matrix-collocation computational system. The method aims to obtain a sustainable approach since it contains the rational structure of the Norlund polynomial. A unique computer program module, which involves very few routines, is constructed to discuss the precision and efficiency of the method and these few steps are described via an algorithm. A residual function is employed in both the error and convergence analyses with mean value theorem for double integrals. The considered equations in the numerical tests stand for model phenomena arising widely in applied sciences. Graphical and numerical comparisons provide a clear observation about the consistency of the method. All results prove that the method is highly accurate, eligible, and provides the ultimate operation for aforementioned problems.Article Citation - WoS: 5Citation - Scopus: 5A Matched Hermite-Taylor Matrix Method To Solve the Combined Partial Integro-Differential Equations Having Nonlinearity and Delay Terms(SPRINGER HEIDELBERG, 2020-09-24) Yalçın, Elif; Kürkçü, Ömür Kıvanç; Sezer, MehmetIn this study, a matched numerical method based on Hermite and Taylor matrix-collocation techniques is developed to obtain the numerical solutions of a combination of the partial integro-differential equations (PIDEs) under Dirichlet boundary conditions, which involve the nonlinearity, delay and Volterra integral terms. These type equations govern wide variety applications in physical sense. The present method easily constitutes the matrix relations of the linear and nonlinear terms in a considered PIDE, using the eligibilities of the Hermite and Taylor polynomials. It thus directly produces a polynomial solution by eliminating a matrix system of nonlinear algebraic functions gathered from the matrix relations. Besides, the validity and precision of the method are tested on stiff examples by fulfilling several error computations. One can state that the method is fast, validate and productive according to the numerical and graphical resultsArticle Citation - WoS: 6Citation - Scopus: 8A Directly Convergent Numerical Method Based on Orthoexponential Polynomials for Solving Integro-Differential Equations With Variable Coefficients and Infinite Boundary on Half-Line(ELSEVIER, 2021-04-01) Kürkçü, Ömür Kıvanç; Sezer, MehmetIn this study, main concern is focused on numerically solving the integro-differentialdelay equations with variable coefficients and infinite boundary on half-line, proposing a matrix-collocation method based on the orthoexponential polynomials. The method is equipped with the collocation points and the hybridized matrix relations between the orthoexponential and Taylor polynomials, which enable us to convert an integral form with infinite boundary into a mathematical formulation. The method also directly establishes the verification of the existence and uniqueness of this integral form through a convergent result. In order to observe the validity of the method versus its computation limit, an error bound analysis is performed by using the upper bound of the orthoexponential polynomials. A computer module containing main infrastructure of the method is specifically designed and run for providing highly precise results. Thus, the numerical and graphical implementations are completely monitored in table and figures, respectively. Based on the comparisons and findings, one can state that the method is remarkable, dependable, and accurate for approaching the aforementioned equations. (C) 2020 Elsevier B.V. All rights reserved.Article A Novel Numerical Implementation for Solving Time Fractional Telegraph Differential Equations Having Multiple Space and Time Delays Via Delannoy Polynomial(2021-04-30) Kürkçü, Ömür KıvançThis paper is concerned with solving numerically the time fractional telegraph equations having multiple space and time delays by proposing a novel matrix-collocation method dependent on the Delannoy polynomial. This method enables easy and fast approximation tool consisting of the matrix expansions of the functions using only the Delannoy polynomial. Thus, the solutions are obtained directly from a unique matrix system. Also, the residual error computation, which involves the same procedure as the method, provides the improvement of the solutions. The method is evaluated under some valuable error tests in the numerical applications. To do this, a unique computer module is devised. The present results are compared with those of the existing methods in the literature, in order to oversee the precision and efficiency of the method. One can express that the proposed method admits very consistent approximation for the equations in question.Article Citation - Scopus: 1A Streamlined Numerical Method To Treat Fractional Nonlinear Terminal Value Problems With Multiple Delays Appearing in Biomathematics(Springer Heidelberg, 2023-02-06) Kürkcü, Ömür KıvançIn this study, a computational matrix-collocation method based on the Lagrange interpolation polynomial is specifically streamlined to treat the fractional nonlinear terminal value problems with multiple delays, such as the Hutchinson, the Wazewska-Czyzewska and the Lasota models in biomathematics. To do this, the robust nonlinear terms of which are smoothed to be deployed in the method. The uniqueness analysis of the solution is discussed in terms of the Banach contraction principle. An error analysis technique is non-linearly theorized and applied to improve the solutions. A programme for the method is especially developed. Thus, the outcomes of five fractional model problems constrained by terminal conditions are numerically and graphically evaluated in tables and figures. Based on the investigation of the results, one can claim that the method presents a sustainable and effective mathematical procedure for the aforementioned problems.Article A Hyperaccurate Semi-Analytical Method With Error Bound Analysis for Treating Fractional Integral Equations With Functional Kernels and Variable Delays(Wiley, 2025-05-01) Kurkcu, Omur KivancThis study is concerned with treating the fractional integral equations with functional kernels and variable delays, introducing a hyperaccurate semi-analytical method based on the Stieltjes-Wigert polynomials, matrix expansions, and the Laplace transform. After analytically converting the terms in the governing equation into the matrix expansions of the Stieltjes-Wigert polynomials type at the collocation points, the method gathers these matrices into a unique matrix equation and then readily solves it by an elimination technique. The residual improvement technique is also introduced to correct the obtained solutions. The residual error bound analysis is theoretically proved via algebraical properties and the mean value theorem for fractional integral calculus, respectively. Six model equations are treated via the method, which runs on a devised computer program. Based on the outcomes, the method is straightforward to treat model equations and to encode its mainframe on a mathematical software.