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A Total Variation Diminishing Hopmoc Scheme for Numerical Time Integration of Evolutionary Differential Equations

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Abstract

This paper concentrates on a total variation diminishing Hopmoc scheme for numerical time integration of evolutionary differential equations. The Hopmoc method for numerical integration of parabolic partial differential equations with convective dominance is based on the concept of spatially decomposed meshes used in the Hopscotch method. In addition, the Hopmoc method uses the concept of integration along characteristic lines in a Semi-Lagrangian scheme based on the Modified Method of Characteristics. This work employs Total Variation Diminishing schemes in order to increase accuracy of the Hopmoc method. Thus, this paper shows that the Hopmoc method in conjunction with a Total Variation Diminishing scheme provides effective improvements over the original Hopmoc method.

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Author information

Authors and Affiliations

  1. CEFET-RJ, Rio de Janeiro, RJ, Brazil

    Diego N. Brandão

  2. Universidade Federal de Lavras, Lavras, MG, Brazil

    Sanderson L. Gonzaga de Oliveira

  3. Universidade Federal Fluminense, Niterói, RJ, Brazil

    Mauricio Kischinhevsky

  4. Laboratório Nacional de Computação Científica (LNCC), Petropólis, RJ, Brazil

    Carla Osthoff & Frederico Cabral

Authors
  1. Diego N. Brandão
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  2. Sanderson L. Gonzaga de Oliveira
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  3. Mauricio Kischinhevsky
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  4. Carla Osthoff
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  5. Frederico Cabral
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Corresponding author

Correspondence to Sanderson L. Gonzaga de Oliveira .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. Saint Petersburg State University, Saint Petersburg, Russia

    Elena Stankova

  5. Polytechnic University of Bari, Bari, Italy

    Carmelo M. Torre

  6. University of Minho, Braga, Portugal

    Ana Maria A.C. Rocha

  7. Monash University, Clayton, Victoria, Australia

    David Taniar

  8. Kyushu Sangyo University, Fukuoka shi, Fukuoka, Japan

    Bernady O. Apduhan

  9. Politecnico di Bari, Bari, Italy

    Eufemia Tarantino

  10. Myongji University, Yongin, Korea (Republic of)

    Yeonseung Ryu

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Brandão, D.N., Gonzaga de Oliveira, S.L., Kischinhevsky, M., Osthoff, C., Cabral, F. (2018). A Total Variation Diminishing Hopmoc Scheme for Numerical Time Integration of Evolutionary Differential Equations. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2018. ICCSA 2018. Lecture Notes in Computer Science(), vol 10960. Springer, Cham. https://doi.org/10.1007/978-3-319-95162-1_4

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  • DOI: https://doi.org/10.1007/978-3-319-95162-1_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95161-4

  • Online ISBN: 978-3-319-95162-1

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