On a New Family of Runge-Kutta-Nystrom Pairs of Orders 6(4)

被引：9

作者：

Kovalnogov, Vladislav N. ^{[1
]}

Fedorov, Ruslan, V ^{[1
]}

Generalov, Dmitry A. ^{[1
]}

Tsvetova, Ekaterina, V ^{[1
]}

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

Tsitouras, Charalampos ^{[6
]}

机构：

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

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

[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, Deptartment Civil Engn, Sect Math, GR-67100 Xanthi, Greece

[6] Natl & Kapodistrian Univ Athens, Gen Deptartment, Euripus Campus, GR-34400 Psachna, Greece

来源：

MATHEMATICS | 2022年 / 10卷 / 06期

关键词：

initial value problem; Runge-Kutta-Nystrom pairs; stability intervals; periodic solutions; 2-STEP METHODS; 9TH ORDER;

D O I：

10.3390/math10060875

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this study, Runge-Kutta-Nystrom pairs of orders 6(4) using six stages per step are considered. The main contribution of the present work is that we introduce a new family of pairs (i.e., new methodology of solution for order conditions) that possesses seven free parameters instead of four, as used by similar pairs until now. Using these extra coefficients efficiently we may construct methods with better properties. Here, we exploit the free parameters in order to derive a pair with extended imaginary stability interval. This type of method may furnish better results on problems with periodic solutions. Extended numerical tests justify our effort.

引用

页数：15

共 24 条

[1] New family for Runge-Kutta-Nystrom pairs of orders 6(4) with coefficients trained to address oscillatory problems
Kovalnogov, Vladislav N.
Kornilova, M., I
Khakhalev, Y. A.
Generalov, D. A.
Simos, T. E.
Tsitouras, Ch
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (12) : 7715 - 7727
[2] Runge-Kutta-Nystrom Pairs of Orders 8(6) for Use in Quadruple Precision Computations
Kovalnogov, Vladislav N.
Matveev, Alexander F.
Generalov, Dmitry A.
Karpukhina, Tamara V.
Simos, Theodore E.
Tsitouras, Charalampos
MATHEMATICS, 2023, 11 (04)
[3] Runge-Kutta-Nystrom Pairs of Orders 8(6) with Coefficients Trained to Perform Best on Classical Orbits
Jerbi, Houssem
Omri, Mohamed
Kchaou, Mourad
Simos, Theodore E.
Tsitouras, Charalampos
MATHEMATICS, 2022, 10 (04)
[4] AN ALGORITHMIC APPROACH TO RUNGE-KUTTA-NYSTROM PAIRS
Kovalnogov, V. N.
Fedorov, R. V.
Karpukhina, T. V.
Evgenievich, C. Y.
Simos, T. E.
Tsitouras, CH.
TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS, 2023, 14 (01): : 3 - 22
[5] On high order Runge-Kutta-Nystrom pairs
Simos, T. E.
Tsitouras, Ch
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2022, 400
[6] Fitted modifications of Runge-Kutta-Nystrom pairs of orders 7(5) for addressing oscillatory problems
Kovalnogov, Vladislav N.
Kornilova, Maria, I
Khakhalev, Yuri A.
Generalov, Dmitry A.
Simos, Theodore E.
Tsitouras, Charalampos
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (01) : 273 - 282
[7] Economical handling of Runge-Kutta-Nystrom step rejection
Kovalnogov, V. N.
Fedorov, R. V.
Karpukhina, M. T.
Kornilova, M. I.
Simos, T. E.
Tsitouras, Ch.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 438
[8] Continuous approximation with embedded Runge-Kutta-Nystrom methods
Baker, TS
Dormand, JR
Prince, PJ
APPLIED NUMERICAL MATHEMATICS, 1999, 29 (02) : 171 - 188
[9] A novel approach on high order Runge-Kutta-Nystrom error estimators
Li, Rong
Lin, Chialiang
Simos, T. E.
Tsitouras, Ch.
APPLIED AND COMPUTATIONAL MATHEMATICS, 2023, 22 (02) : 246 - 258
[10] Fitted modifications of Runge-Kutta pairs of orders 6(5)
Medvedev, Maxim A.
Simos, T. E.
Tsitouras, Ch.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (16) : 6184 - 6194

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