Theta method dynamics

Barclay, G.J. and Griffiths, D.F. and Higham, D.J. (2000) Theta method dynamics. LMS Journal of Computation and Mathematics, 3. pp. 27-43. ISSN 1461-1570 (http://www.lms.ac.uk/jcm/3/lms1999-004/sub/lms1999...)

Abstract

Long-term solutions of the theta method applied to scalar nonlinear differential equations are studied in this paper. In the case where the equation has a stable steady state, lower bounds on the basin of non-oscillatory, monotonic attraction for the theta method are derived. Spurious period two solutions are then analysed. Under mild assumptions, precise results are obtained concerning the generic nature and stability of these solutions for small timesteps. Particular problem classes are studied, and direct connections are made between the existence and stability of period two solutions and the dynamics of the theta method. The analysis is extended to a wide class of semi-discretized partial differential equations. Numerical examples are given.

ORCID iDs

Higham, D.J. ORCID: https://orcid.org/0000-0002-6635-3461

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• Item metadata

  Item type:	Article
  ID code:	177
  Dates:	Date Event 9 February 2000 Published
  Subjects:	Science > Mathematics > Electronic computers. Computer science Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics > Mathematics Faculty of Science > Mathematics and Statistics
  Depositing user:	Ms Sarah Scott
  Date deposited:	03 Mar 2006
  Last modified:	11 Nov 2024 08:15
  Related URLs:	http://www.lms.ac.uk/jcm/
  URI:	https://strathprints.strath.ac.uk/id/eprint/177