IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Regular Section
Boundary Conditions for Numerical Stability Analysis of Periodic Solutions of Ordinary Differential Equations
Sunao MURASHIGE
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Volume E91.A (2008) Issue 4 Pages 1162-1168

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Abstract

This paper considers numerical methods for stability analyses of periodic solutions of ordinary differential equations. Stability of a periodic solution can be determined by the corresponding monodromy matrix and its eigenvalues. Some commonly used numerical methods can produce inaccurate results of them in some cases, for example, near bifurcation points or when one of the eigenvalues is very large or very small. This work proposes a numerical method using a periodic boundary condition for vector fields, which preserves a critical property of the monodromy matrix. Numerical examples demonstrate effectiveness and a drawback of this method.

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© 2008 The Institute of Electronics, Information and Communication Engineers
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