scholarly journals Low rank Runge–Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise

2012 ◽  
Vol 236 (16) ◽  
pp. 3920-3930 ◽  
Author(s):  
Kevin Burrage ◽  
Pamela M. Burrage
Keyword(s):  
Additive Noise ◽  
Low Rank ◽  
Hamiltonian Problems ◽  
Runge Kutta

scholarly journals On a Class of Conjugate Symplectic Hermite-Obreshkov One-Step Methods with Continuous Spline Extension

Axioms ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 58 ◽  
Author(s):  
Francesca Mazzia ◽  
Alessandra Sestini
Keyword(s):  
Differential Equation ◽  
Initial Value Problems ◽  
Multistep Methods ◽  
Maximal Order ◽  
Linear Multistep Methods ◽  
Initial Value ◽  
Hamiltonian Problems ◽  
Efficient Approach ◽  
One Step ◽  
Runge Kutta

The class of A-stable symmetric one-step Hermite–Obreshkov (HO) methods introduced by F. Loscalzo in 1968 for dealing with initial value problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating the differential equation at the mesh points. As a new result, it is shown that these maximal order schemes are conjugate symplectic, which is a benefit when the methods have to be applied to Hamiltonian problems. Furthermore, a new efficient approach for the computation of the spline extension is introduced, adopting the same strategy developed for the BS linear multistep methods. The performances of the schemes are tested in particular on some Hamiltonian benchmarks and compared with those of the Gauss–Runge–Kutta schemes and Euler–Maclaurin formulas of the same order.

A-stability of Runge-Kutta methods for systems with additive noise

1992 ◽  
Vol 32 (4) ◽  
pp. 620-633 ◽  
Author(s):  
Diego Bricio Hernandez ◽  
Renato Spigler
Keyword(s):  
Additive Noise ◽  
Runge Kutta

Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems

2016 ◽  
Vol 21 (1) ◽  
pp. 237-270 ◽  
Author(s):  
Peng Wang ◽  
Jialin Hong ◽  
Dongsheng Xu
Keyword(s):  
Case Studies ◽  
Hamiltonian Systems ◽  
Multiplicative Noise ◽  
Additive Noise ◽  
Symplectic Methods ◽  
Computational Tools ◽  
Stochastic Hamiltonian Systems ◽  
Runge Kutta ◽  
Strong Order

AbstractWe study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems (SHS). Three types of systems, SHS with multiplicative noise, special separable Hamiltonians and multiple additive noise, respectively, are considered in this paper. Stochastic Runge-Kutta (SRK) methods for these systems are investigated, and the corresponding conditions for SRK methods to preserve the symplectic property are given. Based on the weak/strong order and symplectic conditions, some effective schemes are derived. In particular, using the algebraic computation, we obtained two classes of high weak order symplectic Runge-Kutta methods for SHS with a single multiplicative noise, and two classes of high strong order symplectic Runge-Kutta methods for SHS with multiple multiplicative and additive noise, respectively. The numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

scholarly journals Incremental Low Rank Noise Reduction for Robust Infrared Tracking of Body Temperature during Medical Imaging

Electronics ◽  
2019 ◽  
Vol 8 (11) ◽  
pp. 1301 ◽  
Author(s):  
Bardia Yousefi ◽  
Hossein Memarzadeh Sharifipour ◽  
Mana Eskandari ◽  
Clemente Ibarra-Castanedo ◽  
Denis Laurendeau ◽  
...  
Keyword(s):  
Body Temperature ◽  
Medical Imaging ◽  
Noise Reduction ◽  
Additive Noise ◽  
Infrared Imaging ◽  
Tracking System ◽  
Region Of Interest ◽  
Motion Artifacts ◽  
Low Rank ◽  
Value Decomposition

Thermal imagery for monitoring of body temperature provides a powerful tool to decrease health risks (e.g., burning) for patients during medical imaging (e.g., magnetic resonance imaging). The presented approach discusses an experiment to simulate radiology conditions with infrared imaging along with an automatic thermal monitoring/tracking system. The thermal tracking system uses an incremental low-rank noise reduction applying incremental singular value decomposition (SVD) and applies color based clustering for initialization of the region of interest (ROI) boundary. Then a particle filter tracks the ROI(s) from the entire thermal stream (video sequence). The thermal database contains 15 subjects in two positions (i.e., sitting, and lying) in front of thermal camera. This dataset is created to verify the robustness of our method with respect to motion-artifacts and in presence of additive noise (2–20%—salt and pepper noise). The proposed approach was tested for the infrared images in the dataset and was able to successfully measure and track the ROI continuously (100% detecting and tracking the temperature of participants), and provided considerable robustness against noise (unchanged accuracy even in 20% additive noise), which shows promising performance.

scholarly journals Continuous stage stochastic Runge–Kutta methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xuan Xin ◽  
Wendi Qin ◽  
Xiaohua Ding
Keyword(s):  
Differential Equations ◽  
Numerical Experiments ◽  
Additive Noise ◽  
Rooted Tree ◽  
Order Theory ◽  
Order Conditions ◽  
Quadrature Formulas ◽  
General Order ◽  
Runge Kutta ◽  
Theoretical Results

AbstractIn this work, a version of continuous stage stochastic Runge–Kutta (CSSRK) methods is developed for stochastic differential equations (SDEs). First, a general order theory of these methods is established by the theory of stochastic B-series and multicolored rooted tree. Then the proposed CSSRK methods are applied to three special kinds of SDEs and the corresponding order conditions are derived. In particular, for the single integrand SDEs and SDEs with additive noise, we construct some specific CSSRK methods of high order. Moreover, it is proved that with the help of different numerical quadrature formulas, CSSRK methods can generate corresponding stochastic Runge–Kutta (SRK) methods which have the same order. Thus, some efficient SRK methods are induced. Finally, some numerical experiments are presented to demonstrate those theoretical results.

scholarly journals On a Class of Hermite-Obrechkoff One-Step Methods with Continuous Spline Extension

2018 ◽  
Author(s):  
Francesca Mazzia ◽  
Alessandra Sestini
Keyword(s):  
Differential Equation ◽  
Initial Value Problems ◽  
Multistep Methods ◽  
Maximal Order ◽  
Linear Multistep Methods ◽  
Initial Value ◽  
Hamiltonian Problems ◽  
Efficient Approach ◽  
One Step ◽  
Runge Kutta

The class of A-stable symmetric one-step Hermite-Obrechkoff (HO) methods introduced in [1] for dealing with Initial Value Problems is analyzed. Such schemes have the peculiarity of admitting a multiple knot spline extension collocating the differential equation at the mesh points. As a new result, it is shown that these maximal order schemes are conjugate symplectic which is a benefit when the methods have to be applied to Hamiltonian problems. Furthermore a new efficient approach for the computation of the spline extension is introduced, adopting the same strategy developed in [2] for the BS linear multistep methods. The performances of the schemes are tested in particular on some Hamiltonian benchmarks and compared with those of the Gauss Runge-Kutta schemes and Euler-Maclaurin formulas of the same order.

AN ADAPTED SYMPLECTIC INTEGRATOR FOR HAMILTONIAN PROBLEMS

2001 ◽  
Vol 12 (02) ◽  
pp. 225-234 ◽  
Author(s):  
JESÚS VIGO-AGUIAR ◽  
T. E. SIMOS ◽  
A. TOCINO
Keyword(s):  
Numerical Results ◽  
New Method ◽  
Symplectic Integrators ◽  
Order Method ◽  
Symplectic Integrator ◽  
Hamiltonian Problems ◽  
Trigonometric Fitting ◽  
Algebraic Order ◽  
Runge Kutta ◽  
Trigonometrically Fitted Method

In this paper, a new procedure for deriving efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the trigonometric fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge–Kutta–Nyström second algebraic order trigonometrically fitted method is developed. We present explicity the symplecticity conditions for the new modified Runge–Kutta–Nyström method. Numerical results indicate that the new method is much more efficient than the "classical" symplectic Runge–Kutta–Nyström second algebraic order method introduced in Ref. 1.

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