Periodic waveform relaxation of nonlinear dynamic systems by quasi-linearization

• Published in: IEEE transactions on circuits and systems. 1, Fundamental theory and applications Vol. 50; no. 4; pp. 589 - 593
• Main Authors: Yao-Lin Jiang, Chen, R.M.M., Omar Wing
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-04-2003; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Circuit simulation; Nonlinear dynamical systems; Nonlinear equations; Nonlinear systems; Power engineering and energy; Power system analysis computing; Power system dynamics; Radio frequency; Steady-state; Time varying systems
• ISSN: 1057-7122; 1558-1268
• DOI: 10.1109/TCSI.2003.809817

In this brief, we provide an algorithm to treat periodic problems of nonlinear dynamic systems. Our approach is to apply quasi-linearization and waveform relaxation to a system of equations so as to produce a series of linear time-varying systems with periodicity constraints. We prove convergence of the algorithm and apply it to solutions of forced van der Pol equations as a further illustration.