Finite Difference Approximation of Ill-Posed Cauchy Problems

• NISHIDA Kotoba

  Department of Mathematical and Computational Sciences, Faculty of Science, Kagoshima University

• FUJIWARA Hiroshi

  Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University

• ISO Yuusuke

  Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University

Abstract

We consider the finite difference method applied to the initial value problem for a first-order system of linear partial differential equations in the class of analytic functions. We show convergence of a scheme and existence of the analytic solution of the original differential equation by finite difference approximation. The concept of convergence is independent of that of stability as Hayakawa³⁾showed the fact, in 1988, for constant coefficients cases. We deal with a variable coefficients case and develop a theory in which the concept of convergence is independent of that of stability. We give some numerical results with multiple-precision arithmetic.

Journal

• Theoretical and Applied Mechanics Japan

  Theoretical and Applied Mechanics Japan 57 (0), 405-410, 2009

  National Committee for IUTAM

Details

• CRID: 1390001205209540224
• NII Article ID: 130004463704
• DOI: 10.11345/nctam.57.405
• ISSN: 13494244
• ISSN: 13480693
• Text Lang: en
• Data Source:
  • JaLC
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed