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In this work, the simple harmonic oscillator is generalized considering the derivative order as a piecewise constant function. We use the Gauss-Legendre quadrature method to obtain approximate solutions for the associated equation (direct problem). On the other hand, for the inverse problem we use Bayesian statistics to estimate the derivative order and the spring constant, where through the Markov Chain Monte Carlo method the posterior distribution for the parameters is obtained.

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Bayesian Inversion for a Fractional Order Harmonic Oscillator

  • 章节

  • 发表日期：

    2025年

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  • V. R. Olvera-Reyes,
  • M. P. Árciga-Alejandre,
  • J. Sanchez-Ortiz,
  • Y. Peña-Pérez

摘要

In this work, the simple harmonic oscillator is generalized considering the derivative order as a piecewise constant function. We use the Gauss-Legendre quadrature method to obtain approximate solutions for the associated equation (direct problem). On the other hand, for the inverse problem we use Bayesian statistics to estimate the derivative order and the spring constant, where through the Markov Chain Monte Carlo method the posterior distribution for the parameters is obtained.