Ageneral approach for the solution of possibly discontinuous optimization problems by means of pointwise (perhaps smooth) approximations will be proposed. It will be proved that sequences generated by pointwise approx...
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Ageneral approach for the solution of possibly discontinuous optimization problems by means of pointwise (perhaps smooth) approximations will be proposed. It will be proved that sequences generated by pointwise approximation techniques eventually satisfy well justified stopping criteria. Numerical examples will be given.
In this article we present new integral Gronwall-Bellman-Bihari type inequalities for discontinuous functions (integro-sum inequalities). As applications, we investigate estimated solutions for impulsive differential ...
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In this article we present new integral Gronwall-Bellman-Bihari type inequalities for discontinuous functions (integro-sum inequalities). As applications, we investigate estimated solutions for impulsive differential systems, conditions of boundedness, stability, practical stability. (C) 2006 Elsevier Ltd. All rights reserved.
The efficiency of numerical integration of discontinuous functions is a challenge for many different computational methods. To overcome this problem, we introduce an efficient and simple numerical method for the integ...
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The efficiency of numerical integration of discontinuous functions is a challenge for many different computational methods. To overcome this problem, we introduce an efficient and simple numerical method for the integration of discontinuous functions on an arbitrary domain. In the proposed method, the discontinuous function over the domain is replaced by a continuous equivalent function using Legendre polynomials. The method is applicable to all Ansatz spaces with continuous basis functions, and it allows to use standard numerical integration methods in the entire domain. This imposed continuous function is called equivalent Legendre polynomial (ELP). Several numerical examples serve to demonstrate the efficiency and accuracy of the proposed method. Based on 2D and 3D problems of linear elastostatics, the introduced method is further evaluated in the concept of the fictitious domain finite element methods. (C) 2018 Elsevier B.V. All rights reserved.
Fourier transform of discontinuous functions are often encountered in computational electromagnetics and other areas. In this work, a highly accurate, fast conformal Fourier transform (CFT) algorithm is proposed to ev...
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Fourier transform of discontinuous functions are often encountered in computational electromagnetics and other areas. In this work, a highly accurate, fast conformal Fourier transform (CFT) algorithm is proposed to evaluate the finite Fourier transform of 3D discontinuous functions. A curved tetrahedron mesh combined with curvilinear coordinate transform, instead of the Cartesian grid, is adopted to flexibly model an arbitrary shape of the discontinuity boundary. This enables us to take full advantages of high order interpolation and Gaussian quadrature methods to achieve highly accurate Fourier integration results with a low sampling density. The 3D nonuniform fast Fourier transform (NUFFT) helps to keep the complexity of the proposed algorithm to that similar to the traditional 3D FFT algorithm. Therefore, the proposed CFT algorithm can achieve order of magnitude higher accuracy than 3D FFT with lower sampling density and similar computation time. The convergence is proved and verified.
In this paper we investigate a generalized Gronwall-Bellman-Ou-Iang type inequality for piecewise continuous functions. By studying the unknown function in different continuous regions Omega(kj) of Omega, we give the ...
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In this paper we investigate a generalized Gronwall-Bellman-Ou-Iang type inequality for piecewise continuous functions. By studying the unknown function in different continuous regions Omega(kj) of Omega, we give the complete estimate for the unknown function. We apply our result to a boundary value problem of a partial impulsive differential equation for estimation of its solution. (C) 2010 Elsevier Inc. All rights reserved.
In this article, we obtain some new nonlinear integral inequalities for discontinuous functions of two independent variables (Wendroff type) by including also inequalities with delay. We deduce new generalizations of ...
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In this article, we obtain some new nonlinear integral inequalities for discontinuous functions of two independent variables (Wendroff type) by including also inequalities with delay. We deduce new generalizations of earlier results given by R.P. Agarwal, R. Bellman, I. Bihari, B.K. Bondge, V. Lakshmikantham, S. Leela, B.G. Pachpatte for continuous and discrete functions. Furthermore, generalizations ofsome results for integro-sum inequalities are obtained as well. (c) 2006 Elsevier Ltd. All rights reserved.
In this article we investigate some integral functional inequalities of Bellman-Bihari type for piecewise-continuous functions with some fixed points of discontinuity. We also prove a new analogy and generalization of...
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In this article we investigate some integral functional inequalities of Bellman-Bihari type for piecewise-continuous functions with some fixed points of discontinuity. We also prove a new analogy and generalization of results which were obtained by Bellman and Bihari to integro-sum inequalities with delay and discontinuities that do not belong to Lipschitz's type. (c) 2005 Elsevier Ltd. All rights reserved.
This paper investigates integral inequalities with delay for discontinuous functions involving two nonlinear terms. We do not require the classes a"similar to and E center dot in Gallo and Piccirillo's paper ...
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This paper investigates integral inequalities with delay for discontinuous functions involving two nonlinear terms. We do not require the classes a"similar to and E center dot in Gallo and Piccirillo's paper (Bound. Value Probl. 2009:808124, 2009). Our main results can be applied to generalize Gallo and Piccirillo's results and Iovane's results (Nonlinear Anal., Theory Methods Appl. 66:498-508, 2007). Examples to show the bounds of solutions of an impulsive differential equation are also given, which can not be estimated by Gallo and Piccirillo's results.
This paper investigates some new retarded weakly singular integral inequalities with discontinuous functions for two independent variables. The inequalities given here can be used in the qualitative analysis of variou...
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This paper investigates some new retarded weakly singular integral inequalities with discontinuous functions for two independent variables. The inequalities given here can be used in the qualitative analysis of various problems for integral equations and differential equations. Some examples are also given to illustrate the application of the conclusion.
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