A new geometric integration approach based on local invariants

• Matsuda Takeru

  Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo

• Matsuo Takayasu

  Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo

Abstract

In this report we propose a simple new geometric integration approach for solving ordinary differential equations based on the concept of ``local'' invariants. The approach basically belongs to the class of invariants-preserving integrations, but it differs from any existing methods in that it can automatically detect enough number of invariants, and work even for non-conservative systems. Numerical examples show that the approach can in fact work.

Journal

• JSIAM Letters

  JSIAM Letters 5 (0), 37-40, 2013

  The Japan Society for Industrial and Applied Mathematics

Keywords

• conservative method
• local invariant
• discrete gradient method

Details

• CRID: 1390001205299997312
• NII Article ID: 130003371119
• DOI: 10.14495/jsiaml.5.37
• ISSN: 18830617
• ISSN: 18830609
• Web Site: https://www.jstage.jst.go.jp/article/jsiaml/5/0/5_37/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed