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Reinterpretation of Multi-Stage Methods for Stiff Systems: A Comprehensive Review on Current Perspectives and Recommendations

Author

Listed:
  • Yonghyeon Jeon

    (Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
    These authors contributed equally to this work.)

  • Soyoon Bak

    (Department of Mathematics, Kyungpook National University, Daegu 41566, Korea
    These authors contributed equally to this work.)

  • Sunyoung Bu

    (Department of Liberal Arts, Hongik university, Sejong 30016, Korea)

Abstract

In this paper, we compare a multi-step method and a multi-stage method for stiff initial value problems. Traditionally, the multi-step method has been preferred than the multi-stage for a stiff problem, to avoid an enormous amount of computational costs required to solve a massive linear system provided by the linearization of a highly stiff system. We investigate the possibility of usage of multi-stage methods for stiff systems by discussing the difference between the two methods in several numerical experiments. Moreover, the advantages of multi-stage methods are heuristically presented even for nonlinear stiff systems through several numerical tests.

Suggested Citation

  • Yonghyeon Jeon & Soyoon Bak & Sunyoung Bu, 2019. "Reinterpretation of Multi-Stage Methods for Stiff Systems: A Comprehensive Review on Current Perspectives and Recommendations," Mathematics, MDPI, vol. 7(12), pages 1-14, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1158-:d:292844
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