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1

Modelowanie i symulacja cewki nieliniowej ze stratami w żelazie

Kolańska-Płuska J., Grochowicz B.

Prace Instytutu Elektrotechniki

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2016

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Z. 272

217--226

PL

Praca dotyczy badania dynamiki obwodu z cewką nieliniową z uwzględnieniem strat w żelazie. W pracy został przedstawiony model cewki oraz opis za pomocą zmiennych stanu. Przedstawiono również program do badania dynamiki cewki opracowany w środowisku C#, w którym do rozwiązania układu równań różniczkowych nieliniowych modelujących cewkę nieliniową ze stratami w żelazie zastosowano metodę niejawną RADAU IIA różnych rzędów.

EN

Solving rigid differential equations systems should be performed with the application of implicit or semi-explicit methods. As proven in the example given in this paper – the implicit RADAU IIA methods can be successfully applied for the purpose of solving the rigid non-linear systems. The high-order methods up to 11 cause that the application performs relatively large integration steps in pursuit of the steady state that is comparable with the explicit methods. Furthermore, the number of iterations and computation time for a sample non-linear equations formulated for a coil with iron losses is comparable to other methods such as, e.g., multistep Gear method. Also a sample test has proved that the implicit Runge-Kutta methods can be competitive for the purpose of research regarding electrical systems described with the rigid differential equations compared to the multistep Gear method.

2

Modelling of a non-linear coil with loss in iron using the Runge-Kutta methods

Kolańska-Płuska J., Grochowicz B.

Archives of Electrical Engineering

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2016

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Vol. 65, nr 3

527--539

EN

This work presents a study on dynamics of a circuit with a non-linear coil, where loss in iron is also taken into account. A coil model is derived using a state space description. The work also includes the development of an application in C# for coil dynamics examination, where the implicit RADAU IIA method of various orders is applied for the purpose of solving non-linear differential equations modelling the non-linear coil with loss in iron.

3

A Résumé on Interval Runge-Kutta Methods

Marciniak A.

Mathematica Applicanda

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2012

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Vol. 40, No. 1

39-52

EN

The paper presents explicit and implicit interval methods of Runge-Kutta type. Such methods introduce the errors of methods. It means that this kind of errors are included in the interval solutions obtained. Applying these methods for solving the initial value problem in floating-point interval arithmetic we can obtain solutions in the form of intervals which contain all possible numerical errors. Numerical examples are presented.

PL

W artykule przedstawiono jawne i niejawne metody przedziałowe typu Rungego-Kutty. Metody takie zawierają w sobie błędy metod, co oznacza, ze ten rodzaj błędów jest uwzględniony w otrzymywanych rozwiązaniach przedziałowych. Stosując te metody do rozwiązywania zagadnienia początkowego w zmiennopozycyjnej arytmetyce przedziałowej otrzymujemy zatem rozwiązania w postaci przedziałów, które zawierają wszystkie możliwe błędy numeryczne. W artykule przedstawiono także przykłady numeryczne

4

Numerical simulation of NO production in a pulverized coal fired furnace

Straka R., Makovička J., Beneš M.

Environment Protection Engineering

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2011

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Vol. 37, nr 2

13-22

EN

Behaviour of air-coal mixture has been described using the Navier-Stokes equations for the mixture of air and coal particles, accompanied by the turbulence model. The undergoing chemical reactions are described by the Arrhenius kinetics (reaction rate proportional to exp(-E/RT) ). Heat transfer via conduction and radiation has also been considered. The system of partial difference equations is discretized using the finite volume method and the advection upstream splitting method as the Riemann solver. The resulting ordinary differential equations are solved using the 4th order Runge-Kutta method. Results of simulation for typical power production level are presented together with the air staging impact on NO production.

5

Symplectic and time reversible integrator for rigid bodies

Kamberaj H., Low R.J., Neal M.P.

Systems Science

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2003

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Vol. 29, nr 2

31-45

EN

A symplectic and time-reversible molecular dynamics algorithm is presented for rigid molecules in the quaternion representation. The algorithm is developed on the basis of the Trotter factorisation scheme using a Hamiltonian formalism The structure is similar to that of the velocity Verlet algorithm. Subsequently we describe the coupling of the rigid bodies to a thermostat. The isothermal molecular dynamics is defined by introducing additional pseudo-friction coefficients, according to a generalised Nose-Hoover prescription.