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Efficient Time Integration of Nonlinear Partial Differential Equations by Means of Rosenbrock Methods

Author

Listed:
  • Isaías Alonso-Mallo

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, Paseo de Belén 7, 47011 Valladolid, Spain
    Instituto de Investigación en Matemáticas de la Universidad de Valladolid (IMUVa), 47011 Valladolid, Spain.
    These authors contributed equally to this work.)

  • Begoña Cano

    (Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Valladolid, Paseo de Belén 7, 47011 Valladolid, Spain
    Instituto de Investigación en Matemáticas de la Universidad de Valladolid (IMUVa), 47011 Valladolid, Spain.
    These authors contributed equally to this work.)

Abstract

We avoid as as much as possible the order reduction of Rosenbrock methods when they are applied to nonlinear partial differential equations by means of a similar technique to the one used previously by us for the linear case. For this we use a suitable choice of boundary values for the internal stages. The main difference from the linear case comes from the difficulty to calculate those boundary values exactly in terms of data. In any case, the implementation is cheap and simple since, at each stage, just some additional terms concerning those boundary values and not the whole grid must be added to what would be the standard method of lines.

Suggested Citation

  • Isaías Alonso-Mallo & Begoña Cano, 2021. "Efficient Time Integration of Nonlinear Partial Differential Equations by Means of Rosenbrock Methods," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1970-:d:616339
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    Cited by:

    1. Yadira Hernández-Solano & Miguel Atencia, 2022. "Numerical Methods That Preserve a Lyapunov Function for Ordinary Differential Equations," Mathematics, MDPI, vol. 11(1), pages 1-21, December.

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