Error Propagation in Dynamic Iterations Applied to Linear Systems of Differential Equations

B. Zubik-Kowal ()
Additional contact information
B. Zubik-Kowal: Boise State University, 1910 University Drive

Chapter Chapter 31 in Integral Methods in Science and Engineering, 2023, pp 387-400 from Springer

Abstract: Abstract We derive recurrence relations for the errors of dynamic iterations applied to arbitrarily large linear systems of differential equations and address the question of how the physical parameters inherent to these systems influence the convergence of the iterations. The dependence of the recurrence relations on the parameters allows one to conclude and predict how the magnitudes of the parameters slow down or accelerate the rate of convergence. Using the recurrence relations, we conclude that the smaller the magnitudes of the parameters that are multiplied by the previous iterates, the faster the convergence of the dynamic iterations. We also conclude that changes in the magnitude of even a single parameter may lead to changes in the number of iterations needed to get the desired accuracy of numerical approximations. Our theoretical results and predictions are demonstrated by means of numerical experiments.

Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-34099-4_31

Ordering information: This item can be ordered from
http://www.springer.com/9783031340994

DOI: 10.1007/978-3-031-34099-4_31

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().