Long-term analysis of stochastic θ-methods for damped stochastic oscillators

被引：23
作者：
Citro, Vincenzo [1 ]
D'Ambrosio, Raffaele [2 ]
机构：
[1] Univ Salerno, DIIN, Salerno, Italy
[2] Univ LAquila, Dept Engn & Comp Sci & Math, Laquila, Italy
来源：
APPLIED NUMERICAL MATHEMATICS | 2020年 / 150卷
关键词：
Stochastic theta-methods; Stochastic oscillators; Long-term analysis; DIFFERENTIAL-EQUATIONS; NUMERICAL-SIMULATION; STABILITY;
D O I：
10.1016/j.apnum.2019.08.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We analyze long-term properties of stochastic theta-methods for damped linear stochastic oscillators. The presented a-priori analysis of the error in the correlation matrix allows to infer the long-time behaviour of stochastic theta-methods and their capability to reproduce the same long-term features of the continuous dynamics. The theoretical analysis is also supported by a selection of numerical experiments. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
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收藏
页码：18 / 26
页数：9
相关论文
共 28 条
[1]  
[Anonymous], ARXIV190708804
[2]  
Buckwar E., EXPONENTIAL ME UNPUB
[3]   A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods [J].
Buckwar, Evelyn ;
Sickenberger, Thorsten .
MATHEMATICS AND COMPUTERS IN SIMULATION, 2011, 81 (06) :1110-1127
[4]   Numerical methods for second-order stochastic differential equations [J].
Burrage, Kevin ;
Lenane, Ian ;
Lythe, Grant .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2007, 29 (01) :245-264
[5]   Numerical solution of time fractional diffusion systems [J].
Burrage, Kevin ;
Cardone, Angelamaria ;
D'Ambrosio, Raffaele ;
Paternoster, Beatrice .
APPLIED NUMERICAL MATHEMATICS, 2017, 116 :82-94
[6]   Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise [J].
Burrage, Kevin ;
Burrage, Pamela M. .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (16) :3920-3930
[7]   ACCURATE STATIONARY DENSITIES WITH PARTITIONED NUMERICAL METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS [J].
Burrage, Kevin ;
Lythe, Grant .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (03) :1601-1618
[8]   Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise [J].
Burrage, Pamela M. ;
Burrage, Kevin .
NUMERICAL ALGORITHMS, 2014, 65 (03) :519-532
[9]   A spectral method for stochastic fractional differential equations [J].
Cardone, Angelamaria ;
D'Ambrosio, Raffaele ;
Paternoster, Beatrice .
APPLIED NUMERICAL MATHEMATICS, 2019, 139 :115-119
[10]   Stability Issues for Selected Stochastic Evolutionary Problems: A Review [J].
Cardone, Angelamaria ;
Conte, Dajana ;
D'Ambrosio, Raffaele ;
Paternoster, Beatrice .
AXIOMS, 2018, 7 (04)
123