Kürkçü, Ömür Kıvanç
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omur.kivanc@ieu.edu.tr
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02.02. Mathematics
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Sustainable Development Goals
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28
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237
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10
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12
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12
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72
Scopus Citation Count
71
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5
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6
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6.00
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5.92
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7
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Now showing 1 - 10 of 12
Article Citation - WoS: 12Citation - Scopus: 10An Advanced Method With Convergence Analysis for Solving Space-Time Fractional Partial Differential Equations With Multi Delays(Springer Heidelberg, 2019) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, MehmetThis study considers the space-time fractional partial differential equations with multi delays under a unique formulation, proposing a numerical method involving advanced matrix system. This matrix system is made up of the matching polynomial of complete graph together with fractional Caputo and Jumarie derivative types. Also, the derivative types are scrutinized to determine which of them is more proper for the method. Convergence analysis of the method is established via an average value of residual function using double integrals. The obtained solutions are improved with the aid of a residual error estimation. A general computer program module, which contains few steps, is developed. Tables and figures prove the efficiency and simplicity of the method. Eventually, an algorithm is given to illustrate the basis of the method.Article Citation - WoS: 18Citation - Scopus: 17A Numerical Approach Technique for Solving Generalized Delay Integro-Differential Equations With Functional Bounds by Means of Dickson Polynomials(World Scientific Publ Co Pte Ltd, 2018) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, Mehmet; Ilhan, OzgulIn this study, we have considered the linear classes of differential-(difference), integro-differential-(difference) and integral equations by constituting a generalized form, which contains proportional delay, difference, differentiable difference or delay. To solve the generalized form numerically, we use the efficient matrix technique based on Dickson polynomials with the parameter-a along with the collocation points. We also encode the useful computer program for susceptibility of the technique. The residual error analysis is implemented by using the residual function. The consistency of the technique is analyzed. Also, the numerical results illustrated in tables and figures are compared.Article Citation - WoS: 5Citation - Scopus: 7On the Numerical Solution of Fractional Differential Equations With Cubic Nonlinearity Via Matching Polynomial of Complete Graph(Springer India, 2019) Kürkçü, Ömür Kıvanç; Aslan, ErsIn; Sezer, MehmetThis study deals with a generalized form of fractional differential equations with cubic nonlinearity, employing a matrix-collocation method dependent on the matching polynomial of complete graph. The method presents a simple and efficient algorithmic infrastructure, which contains a unified matrix expansion of fractional-order derivatives and a general matrix relation for cubic nonlinearity. The method also performs a sustainable approximation for high value of computation limit, thanks to the inclusion of the matching polynomial in matrix system. Using the residual function, the convergence and error estimation are investigated via the second mean value theorem having a weight function. In comparison with the existing results, highly accurate results are obtained. Moreover, the oscillatory solutions of some model problems arising in several applied sciences are simulated. It is verified that the proposed method is reliable, efficient and productive.Article Citation - WoS: 11Citation - Scopus: 11A Novel Graph-Operational Matrix Method for Solving Multidelay Fractional Differential Equations With Variable Coefficients and a Numerical Comparative Survey of Fractional Derivative Types(Scientific Technical Research Council Turkey-Tubitak, 2019) Kürkçü, ÖmÜr Kıvanç; Aslan, Ersin; Sezer, MehmetIn this study, we introduce multidelay fractional differential equations with variable coefficients in a unique formula. A novel graph-operational matrix method based on the fractional Caputo, Riemann-Liouville, Caputo-Fabrizio, and Jumarie derivative types is developed to efficiently solve them. We also make use of the collocation points and matrix relations of the matching polynomial of the complete graph in the method. We determine which of the fractional derivative types is more appropriate for the method. The solutions of model problems are improved via a new residual error analysis technique. We design a general computer program module. Thus, we can explicitly monitor the usefulness of the method. All results are scrutinized in tables and figures. Finally, an illustrative algorithm is presented.Article Lucas Polynomial Approach for Second Order Nonlinear Differential Equations(2020) Gümgüm, Sevin; Kürkçü, Ömür Kıvanç; Sezer, Mehmet; Bayku S Sava Saner Il, NurcanThis paper presents the Lucas polynomial solution of second-order nonlinearordinary differential equations with mixed conditions. Lucas matrix method is based oncollocation points together with truncated Lucas series. The main advantage of the methodis that it has a simple structure to deal with the nonlinear algebraic system obtained frommatrix relations. The method is applied to four problems. In the first two problems, exactsolutions are obtained. The last two problems, Bratu and Duffing equations are solvednumerically; the results are compared with the exact solutions and some other numericalsolutions. It is observed that the application of the method results in either the exact oraccurate numerical solutions.Article Citation - WoS: 5Citation - Scopus: 4A Numerical Method With a Control Parameter for Integro-Differential Delay Equations With State-Dependent Bounds Via Generalized Mott Polynomial(Springer Heidelberg, 2020) Kürkçü, Ömür KıvançIn this paper, we introduce a numerical method to obtain an accurate approximate solution of the integro-differential delay equations with state-dependent bounds. The method is based basically on the generalized Mott polynomial with the parameter-beta Chebyshev-Lobatto collocation points and matrix structures. These matrices are gathered under a unique matrix equation and then solved algebraically, which produce the desired solution. We discuss the behavior of the solutions, controlling their parameterized form via beta and so we monitor the effectiveness of the method. We improve the obtained solutions by employing the Mott-residual error estimation. In addition to comparing the results in tables, we also illustrate the solutions in figures, which are made up of the phase plane, logarithmic and standard scales. All results indicate that the present method is simple-structured, reliable and straightforward to write a computer program module on any mathematical software.Article The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics(2019) Kürkçü, Ömür Kıvanç; Dönmez Demir, Duygu; Sezer, Mehmet; Çınardalı, TuğçeIn this study, the Legendre operational matrix method based on collocation points is introduced to solve high order ordinary differentialequations with some nonlinear terms arising in physics and mechanics. This technique transforms the nonlinear differential equationinto a matrix equation with unknown Legendre coefficients via mixed conditions. This solution of this matrix equation yields theLegendre coefficients of the solution function. Thus, the approximate solution is obtained in terms of Legendre polynomials. Some testproblems together with residual error estimation are given to show the usefulness and applicability of the method and the numericalresults are compared.Article Citation - WoS: 10Citation - Scopus: 11An Inventive Numerical Method for Solving the Most General Form of Integro-Differential Equations With Functional Delays and Characteristic Behavior of Orthoexponential Residual Function(Springer Heidelberg, 2019) Kürkçü, Ömür Kıvanç; Aslan, Ersin; Sezer, MehmetIn this study, we constitute the most general form of functional integro-differential equations with functional delays. An inventive method based on Dickson polynomials with the parameter- along with collocation points is employed to solve them. The stability of the solutions is simulated according to an interval of the parameter-. A useful computer program is developed to obtain the precise values from the method. The residual error analysis is used to improve the obtained solutions. The characteristic behavior of the residual function is established with the aid of the orthoexponential polynomials. We compare the present numerical results of the method with those obtained by the existing methods in tables.Article A NEW NUMERICAL METHOD FOR SOLVING DELAY INTEGRAL EQUATIONS WITH VARIABLE BOUNDS BY USING GENERALIZED MOTT POLYNOMIALS(2018) Kürkçü, Ömür KıvançIn this study, the delay integral equations with variable bounds are considered and their approximate solutions are obtained byusing a new numerical method based on matrices, collocation points and the generalized Mott polynomials including aparameter- ? . An error analysis technique consisting of the residual function is performed. The numerical examples are appliedto illustrate the practicability and usability of the method. The behavior of the solutions is monitored in terms of the parameter-? . The accuracy of the method is scrutinized for different values of N and also the numerical results are discussed in figuresand tables.Article Citation - WoS: 3Citation - Scopus: 3A Reduced Computational Matrix Approach With Convergence Estimation for Solving Model Differential Equations Involving Specific Nonlinearities of Quartic Type(Scientific Technical Research Council Turkey-Tubitak, 2020) Kürkçü, ÖmÜr KıvançThis study aims to efficiently solve model differential equations involving specific nonlinearities of quartic type by proposing a reduced computational matrix approach based on the generalized Mott polynomial. This method presents a reduced matrix expansion of the generalized Mott polynomial with the parameter-alpha, matrix equations, and Chebyshev-Lobatto collocation points. The simplicity of the method provides fast computation while eliminating an algebraic system of nonlinear equations, which arises from the matrix equation. The method also scrutinizes the consistency of the solutions due to the parameter-alpha. The oscillatory behavior of the obtained solutions on long time intervals is simulated via a coupled methodology involving the proposed method and Laplace-Pade technique. The convergence estimation is established via residual function. Numerical and graphical results are indicated to discuss the validity and efficiency of the method.