Perturbed Runge-Kutta methods for mixed precision applications (Record no. 699)

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fixed length control field 01399nam a2200169 a 4500
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20260901030405.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 250101s2020 xx o 000 0 eng d
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Zachary J. Grant
245 10 - TITLE STATEMENT
Title Perturbed Runge-Kutta methods for mixed precision applications
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Name of producer, publisher, distributor, manufacturer arXiv
Date of production, publication, distribution, manufacture, or copyright notice 2020
336 ## - CONTENT TYPE
Content type term text
338 ## - CARRIER TYPE
Carrier type term online resource
520 ## - SUMMARY, ETC.
Summary, etc. In this work we consider a mixed precision approach to accelerate the implemetation of multi-stage methods. We show that Runge-Kutta methods can be designed so that certain costly intermediate computations can be performed as a lower-precision computation without adversely impacting the accuracy of the overall solution. In particular, a properly designed Runge-Kutta method will damp out the errors committed in the initial stages. This is of particular interest when we consider implicit Runge-Kutta methods. In such cases, the implicit computation of the stage values can be considerably faster if the solution can be of lower precision (or, equivalently, have a lower tolerance). We provide a general theoretical additive framework for designing mixed precision Runge-Kutta methods, and use this framework to derive order conditions for such methods. Next, we show how using this approach allows
506 0# - RESTRICTIONS ON ACCESS NOTE
Terms governing access Open access — freely available to read.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://arxiv.org/pdf/2012.13055v1">https://arxiv.org/pdf/2012.13055v1</a>
Link text Read the full paper (PDF)
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      Available online General Yegates University Library Yegates University Library Science and Computing 09/01/2026   YGE000960 09/01/2026 https://arxiv.org/pdf/2012.13055v1 09/01/2026 Research paper — read online