A novel discrete variational derivative method using ``average-difference methods''

• Furihata Daisuke

  Cybermedia Center, Osaka University

• Sato Shun

  Graduate School of Information Science and Technology, the University of Tokyo

• Matsuo Takayasu

  Graduate School of Information Science and Technology, the University of Tokyo

抄録

We consider conservative numerical methods for a certain class of PDEs, for which standard conservative methods are not effective. There, the standard skew-symmetric difference operators indispensable for the discrete conservation law cause undesirable spatial oscillations. In this letter, to circumvent this difficulty, we propose a novel ``average-difference method,'' which is tougher against such oscillations. However, due to the lack of the apparent skew-symmetry, the proof of the discrete conservation law becomes nontrivial. In order to illustrate partially the superiority, we compare the standard and proposed methods for the linear Klein--Gordon equation.

収録刊行物

• JSIAM Letters

  JSIAM Letters 8 (0), 81-84, 2016

  一般社団法人 日本応用数理学会

キーワード

• geometric integration
• conservative systems
• Klein--Gordon equation

詳細情報

• CRID: 1390001205300793600
• NII論文ID: 130005434752
• DOI: 10.14495/jsiaml.8.81
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/8/0/8_81/_pdf
• 本文言語コード: en
• データソース種別:
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