An Algebraic Approach to Guarantee Harmonic Balance Method Using Grobner Base

Masakazu YAGI  Takashi HISAKADO  Kohshi OKUMURA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.9   pp.2442-2449
Publication Date: 2008/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.9.2442
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Analysis, Modelng and Simulation
harmonic balance method,  error bound,  Grobner base,  algebraic representation,  quadratic approximation,  singular point,  

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Harmonic balance (HB) method is well known principle for analyzing periodic oscillations on nonlinear networks and systems. Because the HB method has a truncation error, approximated solutions have been guaranteed by error bounds. However, its numerical computation is very time-consuming compared with solving the HB equation. This paper proposes an algebraic representation of the error bound using Grobner base. The algebraic representation enables to decrease the computational cost of the error bound considerably. Moreover, using singular points of the algebraic representation, we can obtain accurate break points of the error bound by collisions.