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

• Autorzy: Kolańska-Płuska J. , Grochowicz B.

Identyfikatory

DOI

10.1515/aee-2016-0038

• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

non-linear coil; Runge-Kutta method; stiff non-linear differential equations

• Wydawca: Polish Academy of Sciences, Committee on Electrical Engineering
• Czasopismo: Archives of Electrical Engineering
• Rocznik: 2016
• Tom: Vol. 65, nr 3
• Strony: 527--539
• Opis fizyczny: Bibliogr. 8 poz., fig., tab., wz.

Twórcy

autor

Kolańska-Płuska J.

• Opole University of Technology Faculty of Electrical Engineering, Automatic Control and Informatics Prószkowska 76, 45-758 Opole, Poland

autor

Grochowicz B.

• Opole University of Technology Faculty of Electrical Engineering, Automatic Control and Informatics Prószkowska 76, 45-758 Opole, Poland

Bibliografia

• [1] Alexander R., Design and implementation of DIRK integrators for stiff systems, Applied Numerical Mathematics 46(1): 1-17 (2003).
• [2] Kennedy C. A., Carpenter M. H., Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations, Technical report, NASA/TM-2001-211038 NASA (2001).
• [3] Bijl H., Carpenter M. H, Vatsa N. Kennedy C. A., Implicit Time Integration Schemes for the Unsteady Compressible Navier-Stokes Equations: Laminar Flow, Journal of Computational Physics, 179: 313-329 (2002).
• [4] Dormand J. R., Prince P. J., A family of embedded Runge-Kutta formulae, Computation Applied Maths (1980).
• [5] Hairer E., Wanner G., Solving Ordinary Differential Equations II, Stiff and Differential Algebraic Problems, Springer-Verlag (1991).
• [6] Jay L. O. and Braconnier T., A parallelizable preconditioner for the iterative solution of implicit Runge-Kutta-type methods, Journal of Computational and Applied Mathematics 111: 63-76 (1999).
• [7] Butcher J. C., Chen D. J. L., A new type of singly-implicit Runge-Kutta method, Applied Numerical Mathematics (2000).
• [8] de Swart J. B., Söderlind G., On the construction of error estimators for implicit Runge-Kutta methods, Journal of Computational and Applied Mathematics 86: 347-358 (1997).

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.