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1

An accurate and efficient local one-dimensional method for the 3D acoustic wave equation

Wu Mengling, Jiang Yunzhi, Ge Yongbin

Demonstratio Mathematica

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2022

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Vol. 55, nr 1

528--552

EN

We establish an accurate and efficient scheme with four-order accuracy for solving three-dimensional (3D) acoustic wave equation. First, the local one-dimensional method is used to transfer the 3D wave equation into three one-dimensional wave equations. Then, a new scheme is obtained by the Padé formulas for computation of spatial second derivatives and the correction of the truncation error remainder for discretization of temporal second derivative. It is compact and can be solved directly by the Thomas algorithm. Subsequently, the Fourier analysis method and the Lax equivalence theorem are employed to prove the stability and convergence of the present scheme, which shows that it is conditionally stable and convergent, and the stability condition is superior to that of most existing numerical methods of equivalent order of accuracy in the literature. It allows us to reduce computational cost with relatively large time step lengths. Finally, numerical examples have demonstrated high accuracy, stability, and efficiency of our method.

2

Time-optimal control of linear fractional systems with variable coefficients

Matychyn Ivan, Onyshchenko Viktoriia

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 3

375--386

EN

Linear systems described by fractional differential equations (FDEs) with variable coefficients involving Riemann–Liouville and Caputo derivatives are examined in the paper. For these systems, a solution of the initial-value problem is derived in terms of the generalized Peano–Baker series and a time-optimal control problem is formulated. The optimal control problem is treated from the convex-analytical viewpoint. Necessary and sufficient conditions for time-optimal control similar to that of Pontryagin’s maximum principle are obtained. Theoretical results are supported by examples.

3

The Dynamic Model of Plane Mechanism with Variable Ratio

Cink J., Kosucki A.

Mechanics and Mechanical Engineering

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2016

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Vol. 20, nr 4

393--415

EN

The paper contains the proposal how to reduce many–elements plane mechanism with one degree of freedom to chosen axis or line as one–element model of mechanism. Mostly the place of reduction is driving element in rotary motion (for example, shaft of electric motor) or element in linear motion (for example, piston rod of hydraulic cylinder). The way of determining reduced load and reduced mass of the model is described. Presented mathematical description let determine: firstly, required driving torque or force to provide the suitable acceleration when loads of element are known and secondly, the acceleration (angular or linear) of driving element as result of known driving torque or force and loads of element.

4

Brzegowe zagadnienie pola termicznego w żyle i izolacji przewodu DC z warunkiem Hankela zależnym od współrzędnej kątowej

Gołębiowski J., Zaręba M.

Wiadomości Elektrotechniczne

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2014

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R. 82, nr 11

3--7

PL

W artykule przedstawiono analityczno-numeryczna metodę obliczania stacjonarnego pola termicznego w żyle i izolacji przewodu DC. Obliczenia zweryfikowano za pomocą metody elementów skończonych.

EN

The paper presents analytic-numerical method for calculating stationary thermal field in conductor and insulation of DC cable. Calculations were veriﬁed using ﬁnite element method.