Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods
- Argonne National Lab. (ANL), Lemont, IL (United States)
Here, this study introduces new time-stepping strategies with built-in global error estimators. The new methods propagate the defect along with the numerical solution much like solving for the correction or Zadunaisky’s procedure; however, the proposed approach allows for overlapped internal computations and, therefore, represents a generalization of the classical numerical schemes for solving differential equations with global error estimation. The resulting algorithms can be effectively represented as general linear methods. Finally, several explicit self-starting schemes akin to Runge–Kutta methods with global error estimation are introduced, and the theoretical considerations are illustrated in several examples.
- Research Organization:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- Grant/Contract Number:
- AC02-06CH11357
- OSTI ID:
- 1422717
- Journal Information:
- Journal of Computational and Applied Mathematics, Journal Name: Journal of Computational and Applied Mathematics Journal Issue: C Vol. 332; ISSN 0377-0427
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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