General relaxation methods for initial-value problems with application to multistep schemes
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2021-10-28
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Numerical Mathematics Group
Date
2020-10-28Preprint Posting Date
2020-03-06Embargo End Date
2021-10-28Submitted Date
2020-03-06Permanent link to this record
http://hdl.handle.net/10754/662300
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Recently, an approach known as relaxation has been developed for preserving the correct evolution of a functional in the numerical solution of initial-value problems, using Runge–Kutta methods. We generalize this approach to multistep methods, including all general linear methods of order two or higher, and many other classes of schemes. We prove the existence of a valid relaxation parameter and high-order accuracy of the resulting method, in the context of general equations, including but not limited to conservative or dissipative systems. The theory is illustrated with several numerical examples.Citation
Ranocha, H., Lóczi, L., & Ketcheson, D. I. (2020). General relaxation methods for initial-value problems with application to multistep schemes. Numerische Mathematik. doi:10.1007/s00211-020-01158-4Sponsors
Research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST). The project “Application-domain-specific highly reliable IT solutions” has been implemented with the support provided from the National Research, Development and Innovation Fund of Hungary, and financed under the scheme Thematic Excellence Programme no. 2020-4.1.1-TKP2020 (National Challenges Subprogramme).Publisher
Springer Science and Business Media LLCJournal
Numerische MathematikarXiv
2003.03012Additional Links
http://link.springer.com/10.1007/s00211-020-01158-4ae974a485f413a2113503eed53cd6c53
10.1007/s00211-020-01158-4