
Tatjana V. Tomovic MladenovicUniversity of Kragujevac · Department of Mathematics and Informatics
Tatjana V. Tomovic Mladenovic
PhD
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19
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Education
January 2008 - April 2014
Publications
Publications (19)
Let D+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D_+$$\end{document} be defined as D+={z∈C:|z|<1,Imz>0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepacka...
In this paper, we consider the existence of solutions of the nonlinear fractional differential equation boundary-value problem
\begin{align*}
&\D_*^{\alpha}u(t)=f(t,u(t),u'(t),{}^C\D^{\beta}u(t)), \quad 0< t<1,\; 1<\alpha< 2,\; 0<\beta\leqslant1,\\
&u(0)=A, \quad u(1)=Bu(\eta),
\end{align*}
where $0<\eta<1$, $A\geqslant 0$, $B\eta>1$, $\D_*^\alpha$...
In this paper, anti-Gaussian quadrature rules for trigonometric polynomials are introduced. Special attention is paid to an even weight function on [-?, ?). The main properties of such quadrature rules are proved and a numerical method for their construction is presented. That method is based on relations between nodes and weights of the quadrature...
The paper deals with an integral equation arising from a problem in mathematical biology. We propose approximating its solution by Nyström methods based on Gaussian rules and on product integration rules according to the smoothness of the kernel function. In particular, when the latter is weakly singular we propose two Nyström methods constructed b...
In this paper, we establish new results for non-local boundary value problems. In particular, we study a fractional differential equation where the associated integral equation has a kernel that is not bounded above and changes its sign, so that, the positive sign of the possible solutions is generally not ensured. We provide some examples which su...
In this paper we give a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges [Numer. Math., 67 (1994), pp. 271–288] for definite integrals with the same integrand and interval of integration but with different weight functions related to an arbitrary multi-index. We present a numerical method for the co...
In this paper, we investigate a numerical method for the construction of an optimal set of quadrature rules in the sense of Borges (Numer. Math. 67, 271–288, 1994) for two or three definite integrals with the same integrand and interval of integration, but with different weight functions, related to an arbitrary multi-index. The presented method is...
In this paper, first, we consider the existence of a positive solution for the nonlinear fractional differential equation boundary value problem urn:x-wiley:mma:media:mma4105:mma4105-math-0002 where 0≤ λ < 1, C D α is the Caputo's differential operator of order α , and f :[0,1] × [0, ∞ )→[0, ∞ ) is a continuous function. Using some cone theoretic t...
In this paper we consider multiple orthogonal trigonometric polynomials of semi-integer degree, which are necessary for constructing of an optimal set of quadrature rules with an odd number of nodes for trigonometric polynomials in Borges’ sense [Numer. Math. 67 (1994) 271-288]. We prove that such multiple orthogonal trigonometric polynomials satis...
This paper is devoted to the interpolatory quadrature rules with an even number of multiple nodes, which have the maximal trigonometric degree of exactness. For constructing of such quadrature rules we introduce and consider the so-called s- and σ-orthogonal trigonometric polynomials. We present a numerical method for construction of mentioned quad...
In this paper an error estimate for quadrature rules with an even maximal trigonometric degree of exactness (with an odd number of nodes) for
$2\pi -$
periodic integrand, analytic in a circular domain, is given. Theoretical estimate is illustrated by numerical example.
In this paper, we give error estimates for quadrature rules with maximal trigonometric degree of exactness with respect to an even weight function on (-π,π) for integrand analytic in a certain domain of complex plane. Copyright ©2013 John Wiley & Sons, Ltd.
An optimal set of quadrature formulas with an odd number of nodes for trigonometric polynomials in Borges' sense [Numer. Math. 67 (1994), 271-288], as well as trigonometric multiple orthogonal polynomials of semi-integer degree are defined and studied. The main properties of such a kind of orthogonality are proved. Also, an optimal set of quadratur...
In this paper we give error estimates for quadrature rules with maximal
trigonometric degree of exactness with respect to an even weight
function on (-π,π) for integrand analytic in certain domain of
complex plane.
Orthogonal systems of trigonometric polynomials of semi-integer degree with respect to a weight function w(x)w(x) on [0,2π)[0,2π) have been considered firstly by Turetzkii [A.H. Turetzkii, On quadrature formulae that are exact for trigonometric polynomials, East J. Approx. 11 (2005) 337–359 (translation in English from Uchenye Zapiski, Vypusk 1(149...
In this paper we give error bound for quadrature rules of Gaussian type for trigonometric polynomials with respect to the weight function w(x) = 1+cos x, x ∈ (-π,π), for 2π-periodic integrand, analytic in a circular domain. Obtained theoretical bound is checked and illustrated on some numerical examples.