• Title, Summary, Keyword: linear differential equation

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EXISTENCE AND UNIQUENESS THEOREM FOR LINEAR FUZZY DIFFERENTIAL EQUATIONS

  • You, Cuilian;Wang, Gensen
    • East Asian mathematical journal
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    • v.27 no.3
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    • pp.289-297
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    • 2011
  • The introduction of fuzzy differential equation is to deal wit fuzzy dynamic systems. As classical differential equations, it is difficult to find the solutions to all fuzzy differential equations. In this paper an existence and uniqueness theorem for linear fuzzy differential equations is obtained. Moreover, the exact solution to linear fuzzy differential equation is given.

A NEW APPROACH FOR NUMERICAL SOLUTION OF LINEAR AND NON-LINEAR SYSTEMS

  • ZEYBEK, HALIL;DOLAPCI, IHSAN TIMUCIN
    • Journal of applied mathematics & informatics
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    • v.35 no.1_2
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    • pp.165-180
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    • 2017
  • In this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.

Stability Analysis of Linear Uncertain Differential Equations

  • Chen, Xiaowei;Gao, Jinwu
    • Industrial Engineering and Management Systems
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    • v.12 no.1
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    • pp.2-8
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    • 2013
  • Uncertainty theory is a branch of mathematics based on normolity, duality, subadditivity and product axioms. Uncertain process is a sequence of uncertain variables indexed by time. Canonical Liu process is an uncertain process with stationary and independent increments. And the increments follow normal uncertainty distributions. Uncertain differential equation is a type of differential equation driven by the canonical Liu process. Stability analysis on uncertain differential equation is to investigate the qualitative properties, which is significant both in theory and application for uncertain differential equations. This paper aims to study stability properties of linear uncertain differential equations. First, the stability concepts are introduced. And then, several sufficient and necessary conditions of stability for linear uncertain differential equations are proposed. Besides, some examples are discussed.

Eigenstructure Assignment for Linear Time-Varying Systems: a Differential Sylvester Equation Approach (미분 Sylvester 방정식을 이용한 선형 시변 시스템의 고유구조 지정기법)

  • 최재원;이호철
    • Journal of Institute of Control, Robotics and Systems
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    • v.5 no.7
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    • pp.777-786
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    • 1999
  • This work is concerned with the assignment of the desired eigenstructure for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain scheduling control appeared to be the focus of the research efforts. Scheduling of frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, ⅰ) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ⅱ) we also propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon the newly developed notions. The whole design procedure of the proposed eigenstructure assignment scheme is very systematic, and the scheme could be used to determine the stability of linear time-varying systems easily as well as provides a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by a numerical example.

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Some Identities Involving Euler Polynomials Arising from a Non-linear Differential Equation

  • Rim, Seog-Hoon;Jeong, Joohee;Park, Jin-Woo
    • Kyungpook Mathematical Journal
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    • v.53 no.4
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    • pp.553-563
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    • 2013
  • We derive a family of non-linear differential equations from the generating functions of the Euler polynomials and study the solutions of these differential equations. Then we give some new and interesting identities and formulas for the Euler polynomials of higher order by using our non-linear differential equations.

ON ZEROS AND GROWTH OF SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS

  • Kumar, Sanjay;Saini, Manisha
    • Communications of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.229-241
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    • 2020
  • For a second order linear differential equation f" + A(z)f' + B(z)f = 0, with A(z) and B(z) being transcendental entire functions under some restrictions, we have established that all non-trivial solutions are of infinite order. In addition, we have proved that these solutions, with a condition, have exponent of convergence of zeros equal to infinity. Also, we have extended these results to higher order linear differential equations.

A NOTE ON THE APPROXIMATE SOLUTIONS TO STOCHASTIC DIFFERENTIAL DELAY EQUATION

  • KIM, YOUNG-HO;PARK, CHAN-HO;BAE, MUN-JIN
    • Journal of applied mathematics & informatics
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    • v.34 no.5_6
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    • pp.421-434
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    • 2016
  • The main aim of this paper is to discuss the difference between the Euler-Maruyama's approximate solutions and the accurate solution to stochastic differential delay equation. To make the theory more understandable, we impose the non-uniform Lipschitz condition and weakened linear growth condition. Furthermore, we give the pth moment continuous of the approximate solution for the delay equation.