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Some Remarks on a Variational Method for Stiff Differential Equations

Author

Listed:
  • Sergio Amat

    (Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain)

  • María José Legaz

    (Departamento de Construcción Naval, Universidad de Cádiz, 11003 Cádiz, Spain)

  • Pablo Pedregal

    (E.T.S. Ingenieros Industriales, Universidad de Castilla La Mancha, Campus de Ciudad Real, 13005 Ciudad Real, Spain)

Abstract

We have recently proposed a variational framework for the approximation of systems of differential equations. We associated, in a natural way, with the original problem, a certain error functional. The discretization is based on standard descent schemes, and we can use a variable-step implementation. The minimization problem has a unique solution, and the approach has a global convergence. The use of our error-functional strategy was considered by other authors, but using a completely different way to derive the discretization. Their technique was based on the use of an integral form of the Euler equation for a related optimal control problem, combined with an adapted version of the shooting method, and the cyclic coordinate descent method. In this note, we illustrate and compare our strategy to theirs from a numerical point of view.

Suggested Citation

  • Sergio Amat & María José Legaz & Pablo Pedregal, 2019. "Some Remarks on a Variational Method for Stiff Differential Equations," Mathematics, MDPI, vol. 7(5), pages 1-6, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:455-:d:232831
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    References listed on IDEAS

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    1. Amat, Sergio & José Legaz, M. & Pedregal, Pablo, 2015. "A variable step-size implementation of a variational method for stiff differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 118(C), pages 49-57.
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