Taylor’s decomposition on four points for solving third-order linear time-varying systems. (English) Zbl 1298.65107
Summary: In the present paper, the use of three-step difference schemes generated by Taylor’s decomposition on four points for the numerical solutions of third-order time-varying linear dynamical systems is presented. The method is illustrated for the numerical analysis of an up-converter used in communication systems.
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 90B18 | Communication networks in operations research |
| 34A30 | Linear ordinary differential equations and systems |
Keywords:
Taylor’s decomposition on four points; third-order differential equation; three-step difference schemes; approximation order; periodically time-varying systemsReferences:
| [1] | P. Vanassche, G. Gielen, W. Sansen, Time-varying frequency-domain modeling and analysis of phase-locked-loops with sampling phase-frequency detectors, in: Design, Automation and Test in Europe Conference and Exhibition, 2003, pp. 238-243.; P. Vanassche, G. Gielen, W. Sansen, Time-varying frequency-domain modeling and analysis of phase-locked-loops with sampling phase-frequency detectors, in: Design, Automation and Test in Europe Conference and Exhibition, 2003, pp. 238-243. |
| [2] | Chauvet, W.; Lacaze, B.; Roviras, D.; Duverdier, A., Characterization of a set of invertible LPTV filters using circulant matrices, (Proceedings of IEEE International Conference on Acoustics, Speech, and signal Processing, Hong Kong (2003)) · Zbl 1186.94084 |
| [3] | Latrous, A. G.; Memou, A., A three-point boundary value problem with an integral condition for a third-order partial differential equation, Abstract and Applied Analysis, 1, 33-43 (2005) · Zbl 1077.35044 |
| [4] | Demir, A.; Mehrotra, A.; Roychowdhury, J., Phase noise in oscillators: a unifying theory and numerical methods for characterization, (Proceedings of the 35th Annual Conference on Design Automation, California, USA (1998)), 26-31 |
| [5] | Roychowdhury, J., Reduced order modelling of time-varying systems, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 46, 10, 1237-1288 (1999) |
| [6] | Zadeh, L. A., Frequency analysis of variable networks, Proceedings of the Institute of Radio Engineers, 38, 3, 291-299 (1950) |
| [7] | Kundert, K. S.; White, J. K.; Sangiovanni-Vincentelli, A., Steady-State Methods for Simulating Analog and Microwave Circuits (1990), Kluwer Academic Publishers: Kluwer Academic Publishers Boston, Mass, USA · Zbl 0723.94009 |
| [8] | Vanassche, P.; Gielen, G.; Sansen, W., Symbolic modelling of periodically time-varying systems using harmonic transfer matrices, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 21, 9, 1011-1024 (2002) |
| [9] | Gad, E.; Nahhla, M., Efficient model reduction of linear periodically time-varying systems via compressed transient system function, IEEE Transactions on Circuits and Systems I: Regular Papers, 52, 6, 1188-1204 (2005) · Zbl 1374.94897 |
| [10] | Skelboe, S., Computation of the periodic steady-state response of nonlinear networks by extrapolation methods, IEEE Transactions on Circuits and Systems, 27, 3, 161-175 (1980) · Zbl 0431.94045 |
| [11] | Ashyralyev, A.; Sobolevskii, P. E., On the two new approaches for construction of the high order of accuracy difference schemes for the second order differential equations, Functional Differential Equations, 10, 3,4, 333-405 (2003) · Zbl 1053.65054 |
| [12] | Ashyralyev, A.; Sobolevskii, P. E., On the two-step the high order of accuracy difference schemes for the second order differential equations, Proceedings of Dynamic Systems and Applications, 4, 528-535 (2004) · Zbl 1069.65090 |
| [13] | Ashyralyev, A.; Arjmand, D., A note on the Taylor’s decomposition on four points for a third-order differential equation, Applied Mathematics and Computation, 188, 2, 1483-1490 (2007) · Zbl 1130.65068 |
| [14] | Wan, Y.; Roychowdhury, J., Operator based model-order reduction of linear periodically time-varying systems, (Proceedings of 42nd Annual Conference on Design Automation, Anaheim, California, USA (2005)), 391-396 |
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