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Mehmet Sezer - One of the best experts on this subject based on the ideXlab platform.
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A numerical method for solving some model problems arising in science and convergence analysis based on residual function
Applied Numerical Mathematics, 2017Co-Authors: Ömür Kıvanç Kürkçü, Ersin Aslan, Mehmet SezerAbstract:Abstract In this study, we solve some widely-used model problems consisting of linear, nonlinear differential and integral equations, employing Dickson Polynomials with the parameter-α and the collocation points for an efficient matrix method. The convergence of a Dickson Polynomial Solution of the model problem is investigated by means of the residual function. We encode useful computer programs for model problems, in order to obtain the precise Dickson Polynomial Solutions. These Solutions are plotted along with the exact Solutions in figures and the numerical results are compared with other well-known methods in tables.
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improved jacobi matrix method for the numerical Solution of fredholm integro differential difference equations
mathematical sciences, 2016Co-Authors: Mustafa M Bahsi, Ayse Kurt Bahsi, Mehmet Cevik, Mehmet SezerAbstract:This study is aimed to develop a new matrix method, which is used an alternative numerical method to the other method for the high-order linear Fredholm integro-differential-difference equation with variable coefficients. This matrix method is based on orthogonal Jacobi Polynomials and using collocation points. The improved Jacobi Polynomial Solution is obtained by summing up the basic Jacobi Polynomial Solution and the error estimation function. By comparing the results, it is shown that the improved Jacobi Polynomial Solution gives better results than the direct Jacobi Polynomial Solution, and also, than some other known methods. The advantage of this method is that Jacobi Polynomials comprise all of the Legendre, Chebyshev, and Gegenbauer Polynomials and, therefore, is the comprehensive Polynomial Solution technique.
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Müntz-Legendre Polynomial Solutions of Linear Delay Fredholm Integro-Differential Equations and Residual Correction
Mathematical and Computational Applications, 2013Co-Authors: şuayip Yuzbasi, Emrah Gök, Mehmet SezerAbstract:In this paper, we consider the Muntz-Legendre Polynomial Solutions of the linear delay Fredholm integro-differential equations and residual correction. Firstly, the linear delay Fredholm integro-differential equations are transformed into a system of linear algebraic equations by using by the matrix operations of the Muntz-Legendre Polynomials and the collocation points. When this system is solved, the Muntz- Legendre Polynomial Solution is obtained. Then, an error estimation is presented by means of the residual function and the Muntz-Legendre Polynomial Solutions are improved by the residual correction method. The technique is illustrated by studying the problem for an example. The obtained results show that error estimation and the residual correction method is very effective.
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an improved bessel collocation method with a residual error function to solve a class of lane emden differential equations
Mathematical and Computer Modelling, 2013Co-Authors: şuayip Yuzbasi, Mehmet SezerAbstract:In this study, the modified Bessel collocation method is presented to obtain the approximate Solutions of the linear Lane-Emden differential equations. The method is based on the improvement of the Bessel Polynomial Solutions with the aid of the residual error function. First, the Bessel collocation method is applied to the linear Lane-Emden differential equations and thus the Bessel Polynomial Solutions are obtained. Second, an error problem is constructed by means of the residual error function and this error problem is solved by using the Bessel collocation method. By summing the Bessel Polynomial Solutions of the original problem and the error problem, we have the improved Bessel Polynomial Solutions. When the exact Solution of the problem is not known, the absolute errors can be approximately computed by the Bessel Polynomial Solution of the error problem. In addition, examples that illustrate the pertinent features of the method are presented, and the results of this investigation are discussed.
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taylor Polynomial Solution of hyperbolic type partial differential equations with constant coefficients
International Journal of Computer Mathematics, 2011Co-Authors: Berna Bulbul, Mehmet SezerAbstract:The purpose of this study is to give a Taylor Polynomial approximation for the Solution of hyperbolic type partial differential equations with constant coefficients. The technique used is an improved Taylor matrix method, which has been given for solving ordinary differential, integral and integro-differential equations [M. Gulsu and M. Sezer, A method for the approximate Solution of the high-order linear difference equations in terms of Taylor Polynomials, Int. J. Comput. Math. 82(5) (2005), pp. 629-642; M. Gulsu and M. Sezer, On the Solution of the Riccati equation by the Taylor matrix method, Appl. Math. Comput. 188 (2007), pp. 446-449; A. Karamete and M. Sezer, A Taylor collocation method for the Solution of linear integro-differential equations, Int. J. Comput. Math. 79(9) (2002), pp. 987-1000; N. Kurt and M. Cevik, Polynomial Solution of the single degree of freedom system by Taylor matrix method, Mech. Res. Commun. 35 (2008), pp. 530-536; N. Kurt and M. Sezer, Polynomial Solution of high-order linear Fredholm integro-differential equations with constant coefficients, J. Franklin Inst. 345 (2008), pp. 839-850; S. Nas, S. Yalcinbas, and M. Sezer, A method for approximate Solution of the high-order linear Fredholm integro-differential equations, Int. J. Math. Edu. Sci. Technol. 27(6) (1996), pp. 821-834; M. Sezer, Taylor Polynomial Solution of Volterra integral equations, Int. J. Math. Edu. Sci. Technol. 25(5) (1994), pp. 625-633; M. Sezer, A method for approximate Solution of the second order linear differential equations in terms of Taylor Polynomials, Int. J. Math. Edu. Sci. Technol. 27(6) (1996), pp. 821-834; M. Sezer, M. Gulsu, and B. Tanay, A matrix method for solving high-order linear difference equations with mixed argument using hybrid Legendre and Taylor Polynomials, J. Franklin Inst. 343 (2006), pp. 647-659; S. Yalcinbas, Taylor Polynomial Solutions of nonlinear Volterra-Fredholm integral equation, Appl. Math. Comput. 127 (2002), pp. 196-206; S. Yalcinbas and M. Sezer, The approximate Solution of high-order linear Volterra-Fredholm integro-differential equations in terms of Taylor Polynomials, Appl. Math. Comput. 112 (2000), pp. 291-308]. Some numerical examples, which consist of initial and boundary conditions, are given to illustrate the reliability and efficiency of the method. Also, the results obtained are compared by the known results; the error analysis is performed and the accuracy of the Solution is shown.
Mingfang Zheng - One of the best experts on this subject based on the ideXlab platform.
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guided waves propagation in anisotropic hollow cylinders by legendre Polynomial Solution based on state vector formalism
Composite Structures, 2019Co-Authors: Mingfang Zheng, Yan LyuAbstract:Abstract A spectral approach was presented in the computation of dispersion curves for the general anisotropic hollow cylinders. The derivation is based on the hybrid method of the state-vector formalism and Legendre Polynomials expansion, which was previously adopted for the anisotropic plates. This method will lead to an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles. This hybrid method avoids solving the transcendental dispersion equation. A closed-form Solution for the hollow cylinder, involving multiple integral expressions, is demonstrated. A stable scheme for the integration expansion was established by re-expanding the expansion operators from the first round Legendre Polynomial expansion versus the displacements. Usually, the traditional matrix methods are based on root-finding algorithms, which is difficult to implement in anisotropic tubes. In this research, the hybrid approach we proposed provides a reliable mathematical Solution of wave propagations in an anisotropic hollow cylinder. Applications will be illustrated using isotropic and orthotropic hollow cylinders, in which the isotropic case agrees well with the results by global matrix method. The dispersion curves of orthotropic hollow cylinders, when the out radius set to approximate infinity, are compared to its corresponding anisotropic plate, which is obtained from our previous work. Furthermore, the displacement and stress profiles will be given and analyzed for an orthotropic tube, which has 10 mm thickness with an out radius of 50 mm.
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State-vector formalism and the Legendre Polynomial Solution for modelling guided waves in anisotropic plates
Journal of Sound and Vibration, 2018Co-Authors: Mingfang ZhengAbstract:Abstract We presented a numerical method to solve phase dispersion curve in general anisotropic plates. This approach involves an exact Solution to the problem in the form of the Legendre Polynomial of multiple integrals, which we substituted into the state-vector formalism. In order to improve the efficiency of the proposed method, we made a special effort to demonstrate the analytical methodology. Furthermore, we analyzed the algebraic symmetries of the matrices in the state-vector formalism for anisotropic plates. The basic feature of the proposed method was the expansion of field quantities by Legendre Polynomials. The Legendre Polynomial method avoid to solve the transcendental dispersion equation, which can only be solved numerically. This state-vector formalism combined with Legendre Polynomial expansion distinguished the adjacent dispersion mode clearly, even when the modes were very close. We then illustrated the theoretical Solutions of the dispersion curves by this method for isotropic and anisotropic plates. Finally, we compared the proposed method with the global matrix method (GMM), which shows excellent agreement.
Nurcan Kurt - One of the best experts on this subject based on the ideXlab platform.
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Polynomial Solution of the single degree of freedom system by taylor matrix method
Mechanics Research Communications, 2008Co-Authors: Nurcan Kurt, Mehmet CevikAbstract:Abstract Free vibration of a single degree of freedom system is a fundamental topic in mechanical vibrations. The present study introduces a novel and simple numerical method for the Solution of this system in terms of Taylor Polynomials in the matrix form. Particular and general Solutions of the differential equation can be determined by this method. The method is illustrated by a numerical application and the results obtained are compared with those of the exact Solution.
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Polynomial Solution of high order linear fredholm integro differential equations with constant coefficients
Journal of The Franklin Institute-engineering and Applied Mathematics, 2008Co-Authors: Nurcan Kurt, Mehmet SezerAbstract:In this study, a practical matrix method is presented to find an approximate Solution of high-order linear Fredholm integro-differential equations with constant coefficients under the initial-boundary conditions in terms of Taylor Polynomials. The method converts the integro-differential equation to a matrix equation, which corresponds to a system of linear algebraic equations. Error analysis and illustrative examples are included to demonstrate the validity and applicability of the technique.
Huibert Kwakernaak - One of the best experts on this subject based on the ideXlab platform.
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Polynomial Solution of the standard H 2 problem
2001 European Control Conference (ECC), 2001Co-Authors: Huibert KwakernaakAbstract:A Polynomial Solution to the standard linear H 2 problem is given, together with a detailed algorithm. The assumptions are very general and the paper includes necessary and sufficient conditions for the existence of a Solution.
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PROGRESS IN THE Polynomial Solution OF THE STANDARD H∞ OPTIMAL CONTROL PROBLEM
Automatic Control 1990, 1991Co-Authors: Huibert KwakernaakAbstract:The paper presents the Polynomial Solution of the “standard” H∞ optimal control problem. By J-spectral factorization a pair of matrix Polynomial equations is obtained, one linear, the other quadratic. The Solution of the optimal control problem is reduced to finding a suitable Solution of these equations.
R Sever - One of the best experts on this subject based on the ideXlab platform.
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Polynomial Solution of pt non pt symmetric and non hermitian generalized woods saxon potential via nikiforov uvarov method
arXiv: Quantum Physics, 2008Co-Authors: Sameer M Ikhdair, R SeverAbstract:Using the Nikiforov-Uvarov method, the bound state energy eigenvalues and eigenfunctions of the PT-/non-PT-symmetric and non-Hermitian generalized Woods-Saxon (WS) potential with the real and complex-valued energy levels are obtained in terms of the Jacobi Polynomials. According to the PT-symmetric quantum mechanics, we exactly solved the time-independent Schrodinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.
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Polynomial Solution of non central potentials
arXiv: Quantum Physics, 2007Co-Authors: Sameer M Ikhdair, R SeverAbstract:We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.
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exact Polynomial Solution of cal p cal t non cal p cal t symmetric and non hermitian modified woods saxon potential by the nikiforov uvarov method
International Journal of Theoretical Physics, 2007Co-Authors: Sameer M Ikhdair, R SeverAbstract:Using the Nikiforov–Uvarov (NU) method, the bound state energy eigenvalues and eigenfunctions of the \({\cal P{\cal T}}$-/non-${\cal P}{\cal T}\)-symmetric and non-Hermitian modified Woods–Saxon (WS) model potential with the real and complex-valued energy levels are obtained in terms of the Jacobi Polynomials. According to the \({\cal P}{\cal T}\)-symmetric quantum mechanics, we exactly solved the time-independent Schrodinger equation with same potential for the s-states and also for any l-state as well. It is shown that the results are in good agreement with the ones obtained before.