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On a Variational Method for Stiff Differential Equations Arising from Chemistry Kinetics

Author

Listed:
  • Sergio Amat

    (Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 11003 Cádiz, Spain)

  • María José Legaz

    (Departamento de Construcción Naval, Universidad de Cádiz, 30203 Cartagena, Spain)

  • Juan Ruiz-Álvarez

    (Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 11003 Cádiz, Spain)

Abstract

For the approximation of stiff systems of ODEs arising from chemistry kinetics, implicit integrators emerge as good candidates. This paper proposes a variational approach for this type of systems. In addition to introducing the technique, we present its most basic properties and test its numerical performance through some experiments. The main advantage with respect to other implicit methods is that our approach has a global convergence. The other approaches need to ensure convergence of the iterative scheme used to approximate the associated nonlinear equations that appear for the implicitness. Notice that these iterative methods, for these nonlinear equations, have bounded basins of attraction.

Suggested Citation

  • Sergio Amat & María José Legaz & Juan Ruiz-Álvarez, 2019. "On a Variational Method for Stiff Differential Equations Arising from Chemistry Kinetics," Mathematics, MDPI, vol. 7(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:459-:d:233122
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