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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Data availability
The coefficients of the new Runge–Kutta pair can be retrieved from http://users.uoa.gr/~tsitourasc/t98.m
Code Availability
The Mathematica package reported in section 2 can be retrieved from http://users.uoa.gr/~tsitourasc/t98.m
An alternative Mathematica module can be found in http://users.uoa.gr/~tsitourasc/rk98.m
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The research was supported by a Mega Grant from the Government of the Russian Federation within the framework of the federal project No. 075-15-2021-584.
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Kovalnogov, V.N., Fedorov, R.V., Karpukhina, T.V. et al. Runge–Kutta pairs of orders 9(8) for use in quadruple precision computations. Numer Algor 95, 1905–1919 (2024). https://doi.org/10.1007/s11075-023-01632-8
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DOI: https://doi.org/10.1007/s11075-023-01632-8