Browsing by Author "Toker, Batuhan"

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Haar wavelet collocation method for linear first order stiff differential equations
(E D P SCIENCES17 AVE DU HOGGAR PARC D ACTIVITES COUTABOEUF BP 112, F-91944 CEDEX A, FRANCE, 2020) Atay, Mehmet Tarik; Mertaslan, Onur Metin; Agca, Musa Kasim; Yilmaz, Abdulkadir; Toker, Batuhan; AGÜ, Mühendislik Fakültesi, Makine Mühendisliği Bölümü; Atay, Mehmet Tarık; Mertaslan, Onur Metin; Ağca, Musa Kasım; Yılmaz, Abdulkadir
In 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.
The Numerical Solutions for Stiff Ordinary Differential Equations by Using Interpolated Variational Iteration Method with Comparison to Exact Solutions
(AMER INST PHYSICS, 2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA, 2018) Ciftci, Cihan; Cayci, Hatice Sinem Sas; Atay, Mehmet Tarik; Toker, Batuhan; Guncan, Berkay; Yildirim, Afsin Talha; AGÜ, Mühendislik Fakültesi, Makine Mühendisliği Bölümü
Recently proposed Interpolated Variational Iteration Method (IVIM) is used to find numerical solutions of stiff ordinary differential equations for both linear and nonlinear problems. The examples are given to illustrate the accuracy and effectiveness of IVIM method and IVIM results are compared with exact results. In recent analytical approximate methods based studies related to stiff ordinary differential equations, problems were solved by Adomian Decomposition Method and VIM and Homotopy Perturbation Method, Homotopy Analysis Method etc. In this study comparisons with exact solutions reveal that the Interpolated Variational Iteration Method (IVIM) is easy to implement. In fact, this method is promising methods for various systems of linear and nonlinear stiff ordinary differential equations as an initial value problem. Furthermore, IVIM is giving very satisfactory solutions when compared to exact solutions for nonlinear cases depending on the stiffness ratio of the stiff system to be solved.