Mostrando recursos 1 - 20 de 374

  1. A Novel Method for Solving Nonlinear Volterra Integro-Differential Equation Systems

    Hossein Daliri Birjandi, Mohammad; Saberi-Nadjafi, Jafar; Ghorbani, Asghar
    An efficient iteration method is introduced and used for solving a type of system of nonlinear Volterra integro-differential equations. The scheme is based on a combination of the spectral collocation technique and the parametric iteration method. This method is easy to implement and requires no tedious computational work. Some numerical examples are presented to show the validity and efficiency of the proposed method in comparison with the corresponding exact solutions.

  2. Multiresolution Analysis Applied to the Monge-Kantorovich Problem

    Sánchez-Nungaray, Armando; González-Flores, Carlos; López-Martínez, Raquiel R.
    We give a scheme of approximation of the MK problem based on the symmetries of the underlying spaces. We take a Haar type MRA constructed according to the geometry of our spaces. Thus, applying the Haar type MRA based on symmetries to the MK problem, we obtain a sequence of transportation problem that approximates the original MK problem for each of MRA. Moreover, the optimal solutions of each level solution converge in the weak sense to the optimal solution of original problem.

  3. The Existence and Structure of Rotational Systems in the Circle

    Ramanathan, Jayakumar
    By a rotational system, we mean a closed subset $X$ of the circle, $\mathbb{T}=\mathbb{R}/\mathbb{Z}$ , together with a continuous transformation $f:X\to X$ with the requirements that the dynamical system $(X,f)$ be minimal and that $f$ respect the standard orientation of $\mathbb{T}$ . We show that infinite rotational systems $(X,f)$ , with the property that map $f$ has finite preimages, are extensions of irrational rotations of the circle. Such systems have been studied when they arise as invariant subsets of certain specific mappings, $F:\mathbb{T}\to \mathbb{T}$ . Because our main result makes no explicit mention of a global transformation on $\mathbb{T}$ ,...

  4. Generalized Fractional Integral Operators Involving Mittag-Leffler Function

    Amsalu, Hafte; Suthar, D. L.
    The aim of this paper is to study various properties of Mittag-Leffler (M-L) function. Here we establish two theorems which give the image of this M-L function under the generalized fractional integral operators involving Fox’s $H$ -function as kernel. Corresponding assertions in terms of Euler, Mellin, Laplace, Whittaker, and $K$ -transforms are also presented. On account of general nature of M-L function a number of results involving special functions can be obtained merely by giving particular values for the parameters.

  5. Controllability and Observability of Nonautonomous Riesz-Spectral Systems

    Sutrima, Sutrima; Indrati, Christiana Rini; Aryati, Lina
    There are many industrial and biological reaction diffusion systems which involve the time-varying features where certain parameters of the system change during the process. A part of the transport-reaction phenomena is often modelled as an abstract nonautonomous equation generated by a (generalized) Riesz-spectral operator on a Hilbert space. The basic problems related to the equations are existence of solutions of the equations and how to control dynamical behaviour of the equations. In contrast to the autonomous control problems, theory of controllability and observability for the nonautonomous systems is less well established. In this paper, we consider some relevant aspects regarding...

  6. The Implementation of Milstein Scheme in Two-Dimensional SDEs Using the Fourier Method

    Alnafisah, Yousef
    Multiple stochastic integrals of higher multiplicity cannot always be expressed in terms of simpler stochastic integrals, especially when the Wiener process is multidimensional. In this paper we describe how the Fourier series expansion of Wiener process can be used to simulate a two-dimensional stochastic differential equation (SDE) using Matlab program. Our numerical experiments use Matlab to show how our truncation of Itô’-Taylor expansion at an appropriate point produces Milstein method for the SDE.

  7. ${C}^{\mathrm{1}}$ Hermite Interpolation with PH Curves Using the Enneper Surface

    Lee, Hyun Chol; Kong, Jae Hoon; Kim, Gwangil
    We show that the geometric and PH-preserving properties of the Enneper surface allow us to find PH interpolants for all regular ${C}^{\mathrm{1}}$ Hermite data-sets. Each such data-set is satisfied by two scaled Enneper surfaces, and we can obtain four interpolants on each surface. Examples of these interpolants were found to be better, in terms of bending energy and arc-length, than those obtained using a previous PH-preserving mapping.

  8. A Deposition Model: Riemann Problem and Flux-Function Limits of Solutions

    Cheng, Hongjun; Li, Shiwei
    The Riemann solutions of a deposition model are shown. A singular flux-function limit of the obtained Riemann solutions is considered. As a result, it is shown that the Riemann solutions of the deposition model just converge to the Riemann solutions of the limit system, the scalar conservation law with a linear flux function involving discontinuous coefficient. Especially, for some initial data, the two-shock Riemann solution of the deposition model tends to the delta-shock Riemann solution of the limit system; by contrast, for some initial data, the two-rarefaction-wave Riemann solution of the deposition model tends to the vacuum Riemann solution of...

  9. A Version of Uncertainty Principle for Quaternion Linear Canonical Transform

    Bahri, Mawardi; Resnawati; Musdalifah, Selvy
    In recent years, the two-dimensional (2D) quaternion Fourier and quaternion linear canonical transforms have been the focus of many research papers. In the present paper, based on the relationship between the quaternion Fourier transform (QFT) and the quaternion linear canonical transform (QLCT), we derive a version of the uncertainty principle associated with the QLCT. We also discuss the generalization of the Hausdorff-Young inequality in the QLCT domain.

  10. Optimal Rational Approximations by the Modified Fourier Basis

    Poghosyan, Arnak V.; Bakaryan, Tigran K.
    We consider convergence acceleration of the modified Fourier expansions by rational trigonometric corrections which lead to modified-trigonometric-rational approximations. The rational corrections contain some unknown parameters and determination of their optimal values for improved pointwise convergence is the main goal of this paper. The goal was accomplished by deriving the exact constants of the asymptotic errors of the approximations with further elimination of the corresponding main terms by appropriate selection of those parameters. Numerical experiments outline the convergence improvement of the optimal rational approximations compared to the expansions by the modified Fourier basis.

  11. On Solvability Theorems of Second-Order Ordinary Differential Equations with Delay

    Yeh, Nai-Sher
    For each ${x}_{\mathrm{0}}\in [\mathrm{0,2}\pi )$ and $k\in \mathbf{N}$ , we obtain some existence theorems of periodic solutions to the two-point boundary value problem ${u}^{\mathrm{\prime }\mathrm{\prime }}(x)+{k}^{\mathrm{2}}u(x-{x}_{\mathrm{0}})+g(x,u(x-{x}_{\mathrm{0}}))=h(x)$ in $(\mathrm{0},\mathrm{2}\pi )$ with $u(\mathrm{0})-u(\mathrm{2}\pi )={u}^{\mathrm{\prime }}(\mathrm{0})-{u}^{\mathrm{\prime }}(\mathrm{2}\pi )=\mathrm{0}$ when $g:(\mathrm{0,2}\pi )\times\mathbf{R}\to \mathbf{R}$ is a Caratheodory function which grows linearly in $u$ as $|u|\to \mathrm{\infty }$ , and $h\in {L}^{\mathrm{1}}(\mathrm{0,2}\pi )$ may satisfy a generalized Landesman-Lazer condition $(\mathrm{1}+\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}(\beta )){\int }_{\mathrm{0}}^{\mathrm{2}\pi }h(x)v(x)dx<{\int }_{v(x)>\mathrm{0}}{g}_{\beta }^{+}(x){|v(x)|}^{\mathrm{1}-\beta }dx+{\int }_{v(x)<\mathrm{0}}{g}_{\beta }^{-}(x){|v(x)|}^{\mathrm{1}-\beta }dx$ for all $v\in N(L)\\{\mathrm{0}\}$ . Here $N(L)$ denotes the subspace of ${L}^{\mathrm{1}}(\mathrm{0,2}\pi )$ spanned by $\mathrm{sin}kx$ and $\mathrm{cos}kx$ , $-\mathrm{1}<\beta \le \mathrm{0}$ , ${g}_{\beta }^{+}(x)={\mathrm{l}\mathrm{i}\mathrm{m}  \mathrm{i}\mathrm{n}\mathrm{f}}_{u\to \mathrm{\infty }}(g(x,u)u/{|u|}^{\mathrm{1}-\beta...

  12. Numerical Simulation for a Three-Dimensional Air Pollution Measurement Model in a Heavy Traffic Area under the Bangkok Sky Train Platform

    Suebyat, Kewalee; Pochai, Nopparat
    Air pollutant levels in Bangkok are generally high in street tunnels. They are particularly elevated in almost closed street tunnels such as an area under the Bangkok sky train platform with high traffic volume where dispersion is limited. There are no air quality measurement stations in the vicinity, while the human population is high. In this research, the numerical simulation is used to measure the air pollutant levels. The three-dimensional air pollution measurement model in a heavy traffic area under the Bangkok sky train platform is proposed. The finite difference techniques are employed to approximate the modelled solutions. The vehicle...

  13. Time Scale Inequalities of the Ostrowski Type for Functions Differentiable on the Coordinates

    Nwaeze, Eze R.; Kermausuor, Seth; Tameru, Ana M.
    In 2016, some inequalities of the Ostrowski type for functions (of two variables) differentiable on the coordinates were established. In this paper, we extend these results to an arbitrary time scale by means of a parameter $\lambda \in [\mathrm{0,1}]$ . The aforementioned results are regained for the case when the time scale $\mathbb{T}=\mathbb{R}$ . Besides extension, our results are employed to the continuous and discrete calculus to get some new inequalities in this direction.

  14. Stability for Linear Volterra Difference Equations in Banach Spaces

    Medina, Rigoberto
    This paper is devoted to studying the existence and stability of implicit Volterra difference equations in Banach spaces. The proofs of our results are carried out by using an appropriate extension of the freezing method to Volterra difference equations in Banach spaces. Besides, sharp explicit stability conditions are derived.

  15. Numerical Simulation of a One-Dimensional Water-Quality Model in a Stream Using a Saulyev Technique with Quadratic Interpolated Initial-Boundary Conditions

    Samalerk, Pawarisa; Pochai, Nopparat
    The one-dimensional advection-diffusion-reaction equation is a mathematical model describing transport and diffusion problems such as pollutants and suspended matter in a stream or canal. If the pollutant concentration at the discharge point is not uniform, then numerical methods and data analysis techniques were introduced. In this research, a numerical simulation of the one-dimensional water-quality model in a stream is proposed. The governing equation is advection-diffusion-reaction equation with nonuniform boundary condition functions. The approximated pollutant concentrations are obtained by a Saulyev finite difference technique. The boundary condition functions due to nonuniform pollutant concentrations at the discharge point are defined by the...

  16. Solution of Sequential Hadamard Fractional Differential Equations by Variation of Parameter Technique

    Matar, Mohammed M.
    We obtain in this article a solution of sequential differential equation involving the Hadamard fractional derivative and focusing the orders in the intervals $(\mathrm{1,2})$ and $(\mathrm{2,3})$ . Firstly, we obtain the solution of the linear equations using variation of parameter technique, and next we investigate the existence theorems of the corresponding nonlinear types using some fixed-point theorems. Finally, some examples are given to explain the theorems.

  17. Two Sufficient Conditions for Convex Ordering on Risk Aggregation

    Zhu, Dan; Yin, Chuancun
    We define new stochastic orders in higher dimensions called weak correlation orders. It is shown that weak correlation orders imply stop-loss order of sums of multivariate dependent risks with the same marginals. Moreover, some properties and relations of stochastic orders are discussed.

  18. Multiobjective Optimization, Scalarization, and Maximal Elements of Preorders

    Bevilacqua, Paolo; Bosi, Gianni; Zuanon, Magalì
    We characterize the existence of (weak) Pareto optimal solutions to the classical multiobjective optimization problem by referring to the naturally associated preorders and their finite (Richter-Peleg) multiutility representation. The case of a compact design space is appropriately considered by using results concerning the existence of maximal elements of preorders. The possibility of reformulating the multiobjective optimization problem for determining the weak Pareto optimal solutions by means of a scalarization procedure is finally characterized.

  19. Generalized Asymptotically Almost Periodic and Generalized Asymptotically Almost Automorphic Solutions of Abstract Multiterm Fractional Differential Inclusions

    N’Guérékata, G. M.; Kostić, Marko
    The main aim of this paper is to investigate generalized asymptotical almost periodicity and generalized asymptotical almost automorphy of solutions to a class of abstract (semilinear) multiterm fractional differential inclusions with Caputo derivatives. We illustrate our abstract results with several examples and possible applications.

  20. Soliton Solutions of the Coupled Schrödinger-Boussinesq Equations for Kerr Law Nonlinearity

    Jawad, Anwar Ja’afar Mohamad; Abu-AlShaeer, Mahmood Jawad
    In this paper, the coupled Schrödinger-Boussinesq equations (SBE) will be solved by the sech, tanh, csch, and the modified simplest equation method (MSEM). We obtain exact solutions of the nonlinear for bright, dark, and singular 1-soliton solution. Kerr law nonlinearity media are studied. Results have proven that modified simple equation method does not produce the soliton solution in general case. Solutions may find practical applications and will be important for the conservation laws for dispersive optical solitons.

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