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Numerical Algorithms

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24-08-2023 | Original Paper

Runge–Kutta pairs of orders 9(8) for use in quadruple precision computations

Authors: Vladislav N. Kovalnogov, Ruslan V. Fedorov, Tamara V. Karpukhina, Theodore E. Simos, Charalampos Tsitouras

Published in: Numerical Algorithms | Issue 4/2024

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Abstract

Runge–Kutta embedded pairs of high algebraic order are frequently utilized when strict tolerances are required. When creating such pairings of orders nine and eight for use in double precision arithmetic, numerous conditions are often satisfied. First and foremost, we strive to keep the coefficients’ magnitudes small to prevent accuracy loss. We may, however, allow greater coefficients when working with quadruple precision. Then, we may build pairs of orders 9 and 8 with significantly smaller truncation errors. In this paper, a novel pair is generated that, as predicted, outperforms state-of-the-art pairs of the same orders in a collection of important problems.

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Title: Runge–Kutta pairs of orders 9(8) for use in quadruple precision computations
Authors: Vladislav N. Kovalnogov
Ruslan V. Fedorov
Tamara V. Karpukhina
Theodore E. Simos
Charalampos Tsitouras
Publication date: 24-08-2023
Publisher: Springer US
Published in: Numerical Algorithms / Issue 4/2024
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI: https://doi.org/10.1007/s11075-023-01632-8

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