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<p>This paper presents a novel method to assess the stability of periodic solutions when a Finite-Difference method is applied to determine the periodic solution. As a particular feature, the proposed method is directly based on the Jacobian matrix used in the Newton-iteration of the FD-scheme. Thus, similar to the shooting method, for very low additional effort the stability assessment may be integrated into the calculation of the periodic solution itself. Similar to Hsu’s method, the presented approach is based on a time-stepping like approximation of the monodromy matrix. However, since it is based on general Runge–Kutta schemes, it allows for flexible control of the convergence order and thus the required step-size of the Finite-Difference method.</p>

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An integrated approach to calculate floquet multipliers using the finite-difference-method

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月13日

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  • Alexander Seifert,
  • Hartmut Hetzler

摘要

This paper presents a novel method to assess the stability of periodic solutions when a Finite-Difference method is applied to determine the periodic solution. As a particular feature, the proposed method is directly based on the Jacobian matrix used in the Newton-iteration of the FD-scheme. Thus, similar to the shooting method, for very low additional effort the stability assessment may be integrated into the calculation of the periodic solution itself. Similar to Hsu’s method, the presented approach is based on a time-stepping like approximation of the monodromy matrix. However, since it is based on general Runge–Kutta schemes, it allows for flexible control of the convergence order and thus the required step-size of the Finite-Difference method.