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Python implementation of the algebraic harmonic balance method for second order ordinary differential equations with polynomial coefficients.

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algebraic_hbm (Algebraic Harmonic Balance Method)

This package provides a Python 3.10 implementation of the algebraic harmonic balance method for second order ordinary differential equations with polynomial coefficients as proposed by [1] and used in [2].

References

  1. Hannes Dänschel and Lukas Lentz. "An Algebraic Representation of the Harmonic Balance Method for Ordinary Differential Equations with Polynomial Coefficients".
  2. Hannes Dänschel, Lukas Lentz, and Utz von Wagner. "Error Measures and Solution Artifacts of the Harmonic Balance Method on the Example of the Softening Duffing Oscillator". In: Journal of Theoretical and Applied Mechanics 62.2 (Apr. 2024), pp. 435–455. DOI: 10.15632/jtam-pl/186718

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