TR Dizin İndeksli Yayınlar Koleksiyonu / TR Dizin Indexed Publications Collection

Permanent URI for this collectionhttps://hdl.handle.net/20.500.14365/4

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Subject: search.filters.subject.Legendre wavelets

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  • Article
    Citation - WoS: 11
    Citation - Scopus: 14
    Legendre Wavelet Solution of High Order Nonlinear Ordinary Delay Differential Equations
    (Scientific Technical Research Council Turkey-Tubitak, 2019-05-29) Gumgum, Sevin; Ersoy Ozdek, Demet; Ozaltun, Gokce; Özdek, Demet Ersoy
    The purpose of this paper is to illustrate the use of the Legendre wavelet method in the solution of high-order nonlinear ordinary differential equations with variable and proportional delays. The main advantage of using Legendre polynomials lies in the orthonormality property, which enables a decrease in the computational cost and runtime. The method is applied to five differential equations up to sixth order, and the results are compared with the exact solutions and other numerical solutions when available. The accuracy of the method is presented in terms of absolute errors. The numerical results demonstrate that the method is accurate, effectual and simple to apply.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 15
    Legendre Wavelet Solution of Neutral Differential Equations With Proportional Delays
    (Springer Heidelberg, 2019-04-01) Gumgum, Sevin; Ersoy Özdek, Demet; Özaltun, Gökçe; Bildik, Necdet; Özdek, Demet Ersoy; Kürkçü, Ömür Kıvanç; Sezer, Mehmet; Savaşaneril, Nurcan Baykuş
    The aim of this paper is to solve neutral differential equations with proportional delays by using Legendre wavelet method. Using orthonormal polynomials is the main advantage of this method since it enables a decrease in the computational cost and runtime. Some examples are displayed to illustrate the efficiency and accuracy of the proposed method. Numerical results are compared with various numerical methods in literature and show that the present method is very effectual in solving neutral differential equations with proportional delays.