The art of fitting ordinary differential equations models to experimental results

Pedro José Sebastião, Maria Jardim Beira, Rui Cordeiro, Anant Kumar, João Carlos Fernandes, António Ferraz, Luís Nobre Gonçalves

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Advanced fitting of ordinary differential equations models to experimental results is presented within the context of different academic levels of students and diverse research fields. In many areas, the analysis of experimental results cannot be restricted to cases where particular solutions of the models' differential equations, valid only for specific limit conditions, apply. In those cases, analytical mathematical equations are not available and a complete description of the systems extends beyond the numerical minimization of statistical estimators, like the chi-square, because it requires solving numerically the models' differential equations. Dedicated fitting procedures that involve the interdependent processes of solving the ordinary differential equations and fitting the numerical solutions to the experimental results are required to obtain the best fitting sets of parameters with consistent physical meaning. A simple, but powerful, web-based ordinary differential equations solver and fitter is presented, and used to analyse both the complete motion of a rigid pendulum and the dynamics of a viral infection.

Original languageEnglish
Article number035807
Pages (from-to)1-18
Number of pages18
JournalEuropean Journal Of Physics
Issue number3
Publication statusPublished - Mar 2022


  • COVID-19
  • differential equations
  • least-squares minimization
  • model fitting
  • nonlinear dynamics
  • physical pendulum


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