WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12573/394
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Conference Object Haar Wavelet Collocation Method for Linear First Order Stiff Differential Equations(EDP Sciences, 2020) Atay, Mehmet Tarik; Mertaslan, Onur Metin; Agca, Musa Kasim; Yilmaz, Abdulkadir; Toker, BatuhanIn general, there are countless types of problems encountered from different disciplines that can be represented by differential equations. These problems can be solved analytically in simpler cases; however, computational procedures are required for more complicated cases. Right at this point, the wavelet-based methods have been using to compute these kinds of equations in a more effective way. The Haar Wavelet is one of the appropriate methods that belongs to the wavelet family using to solve stiff ordinary differential equations (ODEs). In this study, The Haar Wavelet method is applied to stiff differential problems in order to demonstrate the accuracy and efficacy of this method by comparing the exact solutions. In comparison, similar to the exact solutions, the Haar wavelet method gives adequate results to stiff differential problems.Article Citation - WoS: 2Citation - Scopus: 2Analysis of the Motion of a Rigid Rod on a Circular Surface Using Interpolated Variational Iteration Method(Yildiz Technical Univ, 2022) Coskun, Safa Bozkurt; Senturk, Erman; Atay, Mehmet TarikIn this paper, interpolated variational iteration method (IVIM) is applied to investigate the vibration period and steady-state response for the motion of rigid rod rocking back and forth on a circular surface without slipping. The problem can be considered as a strongly nonlinear oscillator. In this solution procedure, analytical variational iteration technique is utilized by evaluating the integrals numerically. The approximate analytical results produced by the presented method are compared with the other existing solutions available in the literature. The advantage of using numerical evaluation of integrals, the method becomes fast convergent and a highly accurate solution can be obtained within seconds. The authors believe that the presented technique has potentially wide application in the other nonlinear oscillation problems.Article Citation - WoS: 3Citation - Scopus: 3A Uniformly Valid Approximation Algorithm for Nonlinear Ordinary Singular Perturbation Problems With Boundary Layer Solutions(Springer int Publ Ag, 2016-03-05) Cengizci, Suleyman; Atay, Mehmet Tarik; Eryilmaz, AytekinThis paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness.Article Citation - WoS: 1Citation - Scopus: 2A Semi-Analytic Method for Solving Singularly Perturbed Twin-Layer Problems With a Turning Point(Vilnius Gediminas Tech Univ, 2023-01-19) Cengizci, Suleyman; Kumar, Devendra; Atay, Mehmet TarikThis computational study investigates a class of singularly perturbed second-order boundary-value problems having dual (twin) boundary layers and simple turning points. It is well-known that the classical discretization methods fail to resolve sharp gradients arising in solving singularly perturbed differential equations as the perturbation (diffusion) parameter decreases, i.e., epsilon -> 0(+). To this end, this paper proposes a semi-analytic hybrid method consisting of a numerical procedure based on finite differences and an asymptotic method called the Successive Complementary Expansion Method (SCEM) to approximate the solution of such problems. Two numerical experiments are provided to demonstrate the method's implementation and to evaluate its computational performance. Several comparisons with the numerical results existing in the literature are also made. The numerical observations reveal that the hybrid method leads to good solution profiles and achieves this in only a few iterations.