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1

Impact of Energy Slope Averaging Methods on Numerical Solution of 1D Steady Gradually Varied Flow

Artichowicz W., Prybytak D.

Archives of Hydro-Engineering and Environmental Mechanics

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2015

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Vol. 62, nr 3-4

101--119

EN

In this paper, energy slope averaging in the one-dimensional steady gradually varied flow model is considered. For this purpose, different methods of averaging the energy slope between cross-sections are used. The most popular are arithmetic, geometric, harmonic and hydraulic means. However, from the formal viewpoint, the application of different averaging formulas results in different numerical integration formulas. This study examines the basic properties of numerical methods resulting from different types of averaging.

2

On nonlinear differential equations in generalized Musielak-Orlicz spaces

Kozlowski W. M.

Commentationes Mathematicae

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2013

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Vol. 53, No. 2

13--33

EN

We consider ordinary differential equations u′(t)+(I−T)u(t)=0, where an unknown function takes its values in a given modular function space being a generalization of Musielak-Orlicz spaces, and T is nonlinear mapping which is nonexpansive in the modular sense. We demonstrate that under certain natural assumptions the Cauchy problem related to this equation can be solved. We also show a process for the construction of such a solution. This result is then linked to the recent results of the fixed point theory in modular function spaces.

3

The evolution of three-dimensional perturbations in a magnetohydrodynamic couette flow

Balagondar P. M., Vijayalakshmi A. R.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 3

627-638

EN

The evolution of three-dimensional disturbances in a magnetohydrodynamic Couette flow is investigated using the initial-value problem approach. The general solution to the linearized equations governing three-dimensional disturbances is obtained by using two-dimensional Fourier transformation and other transformations rather than the traditional normal mode approach. The governing stability equation is solved using both the Fourier method and perturbation method. In the Fourier approach, the stability equation is reduced to Mathieu's equation and a periodic solution is obtained. Perturbation solution is obtained for small values of Alfvén velocity. Here Green's function method is employed to obtain the time evolution of linearized disturbances. A measure of disturbance energy is obtained in the case of square wave pulse for velocity and the magnetic field. The time evolution of the three-dimensional disturbances is obtained in terms of the two Green's function representations, one in the form of a Fourier sine series and the other in the form of sine hyperbolic functions representing the energy of a single component and the total energy of a single component. It is shown graphically that the total energy and the sum of first five components of energy are similar but are of different magnitudes.

4

On integrated Volterra integrodifferential equation of higher order

Pachpatte B. G.

Fasciculi Mathematici

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2008

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Nr 39

47-61

EN

In this paper we study the existence and other properties of solutions of a certain iterated Volterra integrodifferential equation of higher order. The tools employed in the analysis are based on application of the Leray-Schauder alternative and a certain integral inequality which provides explicit bound on the unknown function.

5

Approximate controllability for systems described by right invertible operators

Hoang V. T.

Control and Cybernetics

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2008

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Vol. 37, no 1

39-50

EN

In this paper, we deal with the approximate controllability for linear systems described by right invertible operators in an infinite dimensional Banach space.

6

Enhancement to Lohner's Enclosures for Verified Trajectory Tracing in Dynamical Systems

Kleiner A.

Schedae Informaticae

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2006

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Vol. 15

9-28

EN

The paper presents some improvements of the Lohner's algorithm for the rigorous enclosure of trajectories of an ODE.

7

Polynomial quasisolutions of linear differential-difference equations

Cherepennikov V. B., Ermolaeva P. G.

Opuscula Mathematica

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2006

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Vol. 26, no. 3

431-443

EN

The paper discusses a linear differential-difference equation of neutral type with linear coefficients, when at the initial time moment t = 0 the value of the desired function x(t) is known. The authors are not familiar with any results which would state the solvability conditions for the given problem in the class of analytical functions. A polynomial of some degree N is introduced into the investigation. Then the term "polynomial quasisolution" (PQ-solution) is understood in the sense of appearance of the residual Δ(t) = O(tN), when this polynomial is substituted into the initial problem. The paper is devoted to finding PQ-solutions for the initial-value problem under analysis.

8

The controllability of the system described by right invertible operators with constrained controls

Thi H.

Demonstratio Mathematica

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2006

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Vol. 39, nr 3

599-608

EN

This paper is to deal with the controllability of the linear system described by right invertible operators with constrained controls in Banach space.

9

On Two Families of Implicit Interval Methods of Adams-Moulton Type

Jankowska M., Marciniak A.

Computational Methods in Science and Technology

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2006

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Vol. 12, nr 2

109-113

EN

In our previous paper [1] we have presented implicit interval methods of Adams-Moulton type. It appears that two families of these types of methods exist. We compare both families of methods and present a numerical example.