• 제목/요약/키워드: linear equations

검색결과 2,494건 처리시간 0.019초

Fuzzy finite element method for solving uncertain heat conduction problems

  • Chakraverty, S.;Nayak, S.
    • Coupled systems mechanics
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    • 제1권4호
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    • pp.345-360
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    • 2012
  • In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

A dynamical stochastic finite element method based on the moment equation approach for the analysis of linear and nonlinear uncertain structures

  • Falsone, Giovanni;Ferro, Gabriele
    • Structural Engineering and Mechanics
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    • 제23권6호
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    • pp.599-613
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    • 2006
  • A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

ABS ALGORITHMS FOR DIOPHANTINE LINEAR EQUATIONS AND INTEGER LP PROBLEMS

  • ZOU MEI FENG;XIA ZUN QUAN
    • Journal of applied mathematics & informatics
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    • 제17권1_2_3호
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    • pp.93-107
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    • 2005
  • Based on the recently developed ABS algorithm for solving linear Diophantine equations, we present a special ABS algorithm for solving such equations which is effective in computation and storage, not requiring the computation of the greatest common divisor. A class of equations always solvable in integers is identified. Using this result, we discuss the ILP problem with upper and lower bounds on the variables.

ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF LINEAR IMPULSIVE DIFFERENTIAL EQUATIONS

  • Simeonov, P.S.;Bainov, D.D.
    • 대한수학회보
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    • 제31권1호
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    • pp.1-14
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    • 1994
  • In the recent several years the theory of impulsive differential equations has made a rapid progress (see [1] and [2] and the references there). The questions of stability and periodicity of the solutions of these equations have been elaborated in sufficient details while their asymptotic behaviour has been little studied. In the present paper the asymptotic behaviour of the solutions of linear impulsive differential equations is investigated, generalizing the results of J. W. Macki and J.S. Muldowney, 1970 [3], related to ordinary differential equations without impulses.

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A RESERCH ON NONLINEAR (p, q)-DIFFERENCE EQUATION TRANSFORMABLE TO LINEAR EQUATIONS USING (p, q)-DERIVATIVE

  • ROH, KUM-HWAN;LEE, HUI YOUNG;KIM, YOUNG ROK;KANG, JUNG YOOG
    • Journal of applied mathematics & informatics
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    • 제36권3_4호
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    • pp.271-283
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    • 2018
  • In this paper, we introduce various first order (p, q)-difference equations. We investigate solutions to equations which are linear (p, q)-difference equations and nonlinear (p, q)-difference equations. We also find some properties of (p, q)-calculus, exponential functions, and inverse function.

비선형계획법을 이용한 대규모 선형계획해법의 개발 (Development of Nonlinear Programming Approaches to Large Scale Linear Programming Problems)

  • 장수영
    • 대한산업공학회지
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    • 제17권2호
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    • pp.131-142
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    • 1991
  • The concept of criterion function is proposed as a framework for comparing the geometric and computational characteristics of various nonlinear programming approaches to linear programming such as the method of centers, Karmakar's algorithm and the gravitational method. Also, we discuss various computational issues involved in obtaining an efficient parallel implementation of these methods. Clearly, the most time consuming part in solving a linear programming problem is the direction finding procedure, where we obtain an improving direction. In most cases, finding an improving direction is equivalent to solving a simple optimization problem defined at the current feasible solution. Again, this simple optimization problem can be seen as a least squares problem, and the computational effort in solving the least squares problem is, in fact, same as the effort as in solving a system of linear equations. Hence, getting a solution to a system of linear equations fast is very important in solving a linear programming problem efficiently. For solving system of linear equations on parallel computing machines, an iterative method seems more adequate than direct methods. Therefore, we propose one possible strategy for getting an efficient parallel implementation of an iterative method for solving a system of equations and present the summary of computational experiment performed on transputer based parallel computing board installed on IBM PC.

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A NOTE ON LINEAR IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS

  • Choi, Sung Kyu;Koo, Namjip
    • 충청수학회지
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    • 제28권4호
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    • pp.583-590
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    • 2015
  • This paper deals with linear impulsive fractional differential equations involving the Caputo derivative with non-integer order q. We provide exact solutions of linear impulsive fractional differential equations with constant coefficient by mean of the Mittag-Leffler functions. Then we apply the exact solutions to improve impulsive integral inequalities with singularity.