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.ApproximationWoS Q: search.filters.wosQuartile.Q2

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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: 1
    Citation - Scopus: 1
    Distinguishability of a Source Function in a Time Fractional Inhomogeneous Parabolic Equation With Robin Boundary Condition
    (Hacettepe Univ, Fac Sci, 2016-01-01) Özbilge Kahveci, Ebru; Demir, Ali; Özbilge, Ebru
    This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of input-output mappings in the linear time fractional inhomogeneous parabolic equation D(t)(alpha)u(x, t) = (k(x)u(x))(x) + F(x, t) 0 < alpha <= 1, with Robin boundary conditions u(0, t) = psi(0)(t), u(x)(1,t ) = gamma(u(1, t) - psi(1)(t)). By defining the input-output mappings Phi[.] : K -> C-1[0, T] and Psi[.] : K -> C[0, T] the inverse problem is reduced to the problem of their invertibility. Hence, the main purpose of this study is to investigate the distinguishability of the input-output mappings Phi[.] and Psi[.]. Moreover, the measured output data f(t) and h(t) can be determined analytically by a series representation, which implies that the input-output mappings Phi[.] : K -> C-1[0, T] and Psi[.] : K -> C[0, T] can be described explicitly.