Error Analysis of Explicit TSERKN Methods for Highly Oscillatory Systems

2015 ◽  
pp. 175-192
Author(s):  
Xinyuan Wu ◽  
Kai Liu ◽  
Wei Shi
Keyword(s):  
Error Analysis ◽  
Oscillatory Systems ◽  
Highly Oscillatory ◽  
Highly Oscillatory Systems

scholarly journals Double-Loop Control Structure for Rotary Drum Granulation Loop

Processes ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1423
Author(s):  
Ludmila Vesjolaja ◽  
Bjørn Glemmestad ◽  
Bernt Lie
Keyword(s):  
Control Structure ◽  
Control Strategies ◽  
Double Loop ◽  
The Novel ◽  
Loop Control ◽  
Process Dynamics ◽  
Oscillatory Systems ◽  
Novel Approach ◽  
Highly Oscillatory ◽  
Highly Oscillatory Systems

The operation of granulation plants on an industrial scale is challenging. Periodic instability associated with the operation of the granulation loop causes the particle size distribution of the particles flowing out from the granulator to oscillate, thus making it difficult to maintain the desired product quality. To address this problem, two control strategies are proposed in this paper, including a novel approach, where product-sized particles are recycled back to maintain a stable granulation loop process. A dynamic model of the process that is based on a population balance equation is used to represent the process dynamics. Both of the control strategies utilize a double-loop control structure that is suitable for highly oscillatory systems. The simulation results show that both control strategies, including the novel approach, are able to remove the oscillating behaviour and stabilize the granulation plant loop.

An Essential Extension of the Finite-Energy Condition for Extended Runge-Kutta-Nyström Integrators when Applied to Nonlinear Wave Equations

2017 ◽  
Vol 22 (3) ◽  
pp. 742-764 ◽  
Author(s):  
Lijie Mei ◽  
Changying Liu ◽  
Xinyuan Wu
Keyword(s):  
Error Analysis ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Energy Condition ◽  
Finite Energy ◽  
Nonlinear Wave Equations ◽  
Oscillatory Systems ◽  
Highly Oscillatory ◽  
Runge Kutta ◽  
Erkn Integrators

AbstractThis paper is devoted to an extension of the finite-energy condition for extended Runge-Kutta-Nyström (ERKN) integrators and applications to nonlinear wave equations. We begin with an error analysis for the integrators for multi-frequency highly oscillatory systems , where M is positive semi-definite, . The highly oscillatory system is due to the semi-discretisation of conservative, or dissipative, nonlinear wave equations. The structure of such a matrix M and initial conditions are based on particular spatial discretisations. Similarly to the error analysis for Gaustchi-type methods of order two, where a finite-energy condition bounding amplitudes of high oscillations is satisfied by the solution, a finite-energy condition for the semi-discretisation of nonlinear wave equations is introduced and analysed. These ensure that the error bound of ERKN methods is independent of . Since stepsizes are not restricted by frequencies of M, large stepsizes can be employed by our ERKN integrators of arbitrary high order. Numerical experiments provided in this paper have demonstrated that our results are truly promising, and consistent with our analysis and prediction.

Numerical solution of highly oscillatory ordinary differential equations

Acta Numerica ◽  
1997 ◽  
Vol 6 ◽  
pp. 437-483 ◽  
Author(s):  
Linda R. Petzold ◽  
Laurent O. Jay ◽  
Jeng Yen
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Structural Model ◽  
Circuit Simulation ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Vehicle Simulation ◽  
Oscillatory Systems ◽  
Highly Oscillatory

One of the most difficult problems in the numerical solution of ordinary differential equations (ODEs) and in differential-algebraic equations (DAEs) is the development of methods for dealing with highly oscillatory systems. These types of systems arise, for example, in vehicle simulation when modelling the suspension system or tyres, in models for contact and impact, in flexible body simulation from vibrations in the structural model, in molecular dynamics, in orbital mechanics, and in circuit simulation. Standard numerical methods can require a huge number of time-steps to track the oscillations, and even with small stepsizes they can alter the dynamics, unless the method is chosen very carefully.

The O–C diagrams of minor planets − a new approach to modelling the rotation

1999 ◽  
Vol 173 ◽  
pp. 185-188
Author(s):  
Gy. Szabó ◽  
K. Sárneczky ◽  
L.L. Kiss
Keyword(s):  
Error Analysis ◽  
Time Dependence ◽  
Theoretical Work ◽  
Minor Planet ◽  
Minor Planets ◽  
New Approach ◽  
Preliminary Results ◽  
Ccd Observations

AbstractA widely used tool in studying quasi-monoperiodic processes is the O–C diagram. This paper deals with the application of this diagram in minor planet studies. The main difference between our approach and the classical O–C diagram is that we transform the epoch (=time) dependence into the geocentric longitude domain. We outline a rotation modelling using this modified O–C and illustrate the abilities with detailed error analysis. The primary assumption, that the monotonity and the shape of this diagram is (almost) independent of the geometry of the asteroids is discussed and tested. The monotonity enables an unambiguous distinction between the prograde and retrograde rotation, thus the four-fold (or in some cases the two-fold) ambiguities can be avoided. This turned out to be the main advantage of the O–C examination. As an extension to the theoretical work, we present some preliminary results on 1727 Mette based on new CCD observations.

Error Analysis in Neuropsychological Assessment of Verbal Memory and Learning

1995 ◽  
Vol 11 (1) ◽  
pp. 21-28 ◽  
Author(s):  
Dietmar Heubrock
Keyword(s):  
Error Analysis ◽  
Verbal Memory ◽  
Verbal Learning ◽  
Learning Disorders ◽  
Memory And Learning ◽  
Auditory Verbal Learning Test ◽  
Additional Information ◽  
Auditory Verbal Learning ◽  
Accurate Picture ◽  
Learning Test

Performance on a German version of the Rey Auditory-Verbal Learning Test (AVLT) was investigated for 64 juvenile patients who were subdivided in 6 clinical groups. In addition to standard evaluation of AVLT protocols which is usually confined to items recalled correctly, an error analysis was performed. Differentiating between total errors (TE), repetition errors (RE), and misnamings (ME), substantial differences between clinical groups could be demonstrated. It is argued that error analysis of verbal memory and learning enriches the understanding of neuropsychological syndromes, and provides additional information for diagnostic and clinical use. Thus, it is possible to gain a more accurate picture so that patients can be appropriately retrained, and research into the functional causes of memory and learning disorders can be intensified.

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