Explicit Runge-Kutta Methods Combined with Advanced Versions of the Richardson Extrapolation

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DOI

  • Zahari Zlatev
  • Ivan Dimov, Bulgarian Acad Sci, Bulgarian Academy of Sciences, Inst Informat & Commun Technol, Dept Parallel Algorithms
  • ,
  • Istvan Farago, Budapest Univ Technol & Econ, Budapest University of Technology & Economics, Inst Math
  • ,
  • Krassimir Georgiev, Bulgarian Acad Sci, Bulgarian Academy of Sciences, Inst Informat & Commun Technol, Dept Parallel Algorithms
  • ,
  • Agnes Havasi, Eotvos Lorand Univ, Eotvos Lorand University, Dept Appl Anal & Computat Math

Richardson Extrapolation is a very general numerical procedure, which can be applied in the solution of many mathematical problems in an attempt to increase the accuracy of the results. It is assumed that this approach is used to handle non-linear systems of ordinary differential equations (ODEs) which arise often in the mathematical description of scientific and engineering models either directly or after the discretization of the spatial derivatives of partial differential equations (PDEs). The major topic is the analysis of eight advanced implementations of the Richardson Extrapolation. Two important properties are analyzed: (a) the possibility to achieve more accurate results and (b) the possibility to improve the stability properties of eight advanced versions of the Richardson Extrapolation. A two-parameter family of test-examples was constructed and used to check both the accuracy and the absolute stability of the different versions of the Richardson Extrapolation when these versions are applied together with several Explicit Runge-Kutta Methods (ERKMs).

OriginalsprogEngelsk
TidsskriftComputational Methods in Applied Mathematics
Vol/bind20
Nummer4
Sider (fra-til)739-762
Antal sider24
ISSN1609-4840
DOI
StatusUdgivet - okt. 2020

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