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Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations

Author

Listed:
  • Jürgen Geiser

    (The Institute of Theoretical Electrical Engineering, Ruhr University of Bochum, Universitätsstrasse 150, D-44801 Bochum, Germany)

  • Jose L. Hueso

    (Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Eulalia Martínez

    (Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

Abstract

This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection–diffusion–reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive ideas. Based on shifting the time-steps with additional adaptive time-ranges, we could embedded the adaptive techniques into the splitting approach. The numerical analysis of the adapted iterative splitting schemes is considered and we develop the underlying error estimates for the application of the adaptive schemes. The performance of the method with respect to the accuracy and the acceleration is evaluated in different numerical experiments. We test the benefits of the adaptive splitting approach on highly nonlinear Burgers’ and Maxwell–Stefan diffusion equations.

Suggested Citation

  • Jürgen Geiser & Jose L. Hueso & Eulalia Martínez, 2020. "Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations," Mathematics, MDPI, vol. 8(3), pages 1-22, February.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:302-:d:324700
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    Cited by:

    1. Alexander Sukhinov & Alexander Chistyakov & Inna Kuznetsova & Yulia Belova & Elena Rahimbaeva, 2022. "Development and Research of a Modified Upwind Leapfrog Scheme for Solving Transport Problems," Mathematics, MDPI, vol. 10(19), pages 1-21, September.

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