A Total Variation Diminishing Hopmoc Scheme for Numerical Time Integration of Evolutionary Differential Equations (original) (raw)

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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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
  2. Sanderson L. Gonzaga de Oliveira
  3. Mauricio Kischinhevsky
  4. Carla Osthoff
  5. Frederico Cabral

Corresponding author

Correspondence toSanderson 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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