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

被引：1

作者：

Kovalnogov, Vladislav N. ^{[1
]}

Fedorov, Ruslan V. ^{[1
]}

Karpukhina, Tamara V. ^{[1
]}

Simos, Theodore E. ^{[1
,2
,3
,4
,5
,6
]}

Tsitouras, Charalampos ^{[7
]}

机构：

[1] Ulyanovsk State Tech Univ, Lab Inter Disciplinary Problems Energy Prod, 32 Severny Venetz St, Ulyanovsk 432027, Russia

[2] Gulf Univ Sci & Technol, Ctr Appl Math & Bioinformat, West Mishref 32093, Kuwait

[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[4] Neijiang Normal Univ, Data Recovery Key Lab Sichuan Prov, Neijiang 641100, Peoples R China

[5] Democritus Univ Thrace, Sect Math, Dept Civil Engn, GR-67100 Xanthi, Greece

[6] Univ Western Macedonia, Dept Math, GR-52100 Kastoria, Greece

[7] Natl & Kapodistrian Univ Athens, Gen Dept, Euripus Campus, GR-34400 Athens, Greece

来源：

NUMERICAL ALGORITHMS | 2024年 / 95卷 / 04期

关键词：

Initial value problem; Runge-Kutta; Higher accuracies; INTEGRATION;

D O I：

10.1007/s11075-023-01632-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1905 / 1919

页数：15

共 29 条

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