Splitting methods for non-autonomous linear systems

被引：10

作者：

Blanes, Sergio

Casas, Fernando ^{[1
]}

Murua, Ander

机构：

[1] Univ Politecn Valencia, Inst Matemat Multidiciplinar, E-46022 Valencia, Spain

[2] Univ Jaume 1, Dept Math, E-12071 Castellon de La Plana, Spain

[3] UPV, EHU, Informat Fac, Donostia San Sebastian, Spain

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2007年 / 84卷 / 06期

关键词：

splitting methods; non-autonomous systems; Magnus expansion;

D O I：

10.1080/00207160701458567

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present splitting methods for numerically solving a certain class of explicitly time-dependent linear differential equations. Starting from an efficient method for the autonomous case and making use of the formal solution obtained with the Magnus expansion, we show how to get the order conditions for the non-autonomous case. We also build a family of sixth-order integrators whose performance is clearly superior to previous splitting methods on several numerical examples.

引用

页码：713 / 727

页数：15

共 50 条

[31] The stability of the equilibrium positions of non-linear non-autonomous mechanical systems
Aleksandrov, A. Yu.
PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS, 2007, 71 (03): : 324 - 338
[32] Oscillation for linear non-autonomous systems of difference equations with continuous arguments
Meng, Qiong
Yan, Jurang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (02) : 970 - 976
[33] Spectral and stability questions concerning evolution of non-autonomous linear systems
Nerurkar, MG
PROCEEDINGS OF THE 36TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-5, 1997, : 3926 - 3931
[34] Preservation of exponential stability for linear non-autonomous functional differential systems
Berezansky, Leonid
Braverman, Elena
AUTOMATICA, 2010, 46 (12) : 2077 - 2081
[35] EXPONENTIAL STABILITY CRITERIA OF LINEAR NON-AUTONOMOUS SYSTEMS WITH MULTIPLE DELAYS
Vu Ngoc Phat
Nam, Phan T.
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2005,
[36] Explicit symplectic RKN methods for perturbed non-autonomous oscillators: Splitting, extended and exponentially fitting methods
Blanes, S.
COMPUTER PHYSICS COMMUNICATIONS, 2015, 193 : 10 - 18
[37] Minimal residual multistep methods for large stiff non-autonomous linear problems
Faleichik, Boris V.
1600, Elsevier B.V. (387):
[38] Minimal residual multistep methods for large stiff non-autonomous linear problems
Faleichik, Boris, V
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 387
[39] METHOD FOR THE ACCELERATED ANALYSIS OF THE CHARACTERISTIC EQUATION OF NON-LINEAR NON-AUTONOMOUS SYSTEMS
ABLIN, AN
PEKELIS, MA
RADIOTEKHNIKA I ELEKTRONIKA, 1980, 25 (02): : 428 - 430
[40] ANALYSIS OF NON-LINEAR NON-AUTONOMOUS SYSTEMS BY TRUNCATED POINT-MAPPINGS
FLASHNER, H
GUTTALU, RS
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1989, 24 (04) : 327 - 344

← 1 2 3 4 5 →