B–Series Analysis of Stochastic Runge–Kutta Methods That Use an Iterative Scheme to Compute Their Internal Stage Values

2009 ◽  
Vol 47 (1) ◽  
pp. 181-203 ◽  
Author(s):  
Kristian Debrabant ◽  
Anne KvÆrnØ
Keyword(s):  
Iterative Scheme ◽  
Series Analysis ◽  
Runge Kutta ◽  
Internal Stage

scholarly journals Stability and Fractal Patterns of Complex Logistic Map

2014 ◽  
Vol 14 (3) ◽  
pp. 14-24
Author(s):  
Bhagwati Prasad ◽  
Kuldip Katiyar
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Control Parameter ◽  
Iterative Scheme ◽  
Logistic Map ◽  
One Dimensional ◽  
Series Analysis ◽  
Fractal Patterns

Abstract The intent of this paper is to study the fractal patterns of one dimensional complex logistic map by finding the optimum values of the control parameter using Ishikawa iterative scheme. The logistic map is shown to have bounded and stable behaviour for larger values of the control parameter. This is well depicted via time series analysis and interesting fractal patterns as well are presented

scholarly journals The numerical solution of stochastic differential equations

1977 ◽  
Vol 20 (1) ◽  
pp. 8-12 ◽  
Author(s):  
P. E. Kloeden ◽  
R. A. Pearson
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Numerical Solution ◽  
Stochastic Differential Equations ◽  
Iterative Scheme ◽  
Correction Term ◽  
Second Order ◽  
Runge Kutta ◽  
The Given

AbstractA method is proposed for the numerical solution of Itô stochastic differential equations by means of a second-order Runge–Kutta iterative scheme rather than the less efficient Euler iterative scheme. It requires the Runge–Kutta iterative scheme to be applied to a different stochastic differential equation obtained by subtraction of a correction term from the given one.

Dynamical Peculiarities of Concatenational Changes in Functional Cardiovascular Parameters

2018 ◽  
Vol 3 (82) ◽  
Author(s):  
Eurelija Venskaitytė ◽  
Jonas Poderys ◽  
Tadas Česnaitis
Keyword(s):  
Time Series ◽  
Time Series Analysis ◽  
Functional State ◽  
The Body ◽  
Functional Changes ◽  
High Intensity Training ◽  
Series Analysis ◽  
Greco Roman ◽  
St Segment ◽  
Standard Lead

Research  background  and  hypothesis.  Traditional  time  series  analysis  techniques,  which  are  also  used  for the analysis of cardiovascular signals, do not reveal the relationship between the  changes in the indices recorded associated with the multiscale and chaotic structure of the tested object, which allows establishing short-and long-term structural and functional changes.Research aim was to reveal the dynamical peculiarities of interactions of cardiovascular system indices while evaluating the functional state of track-and-field athletes and Greco-Roman wrestlers.Research methods. Twenty two subjects participated in the study, their average age of 23.5 ± 1.7 years. During the study standard 12 lead electrocardiograms (ECG) were recorded. The following ECG parameters were used in the study: duration of RR interval taken from the II standard lead, duration of QRS complex, duration of JT interval and amplitude of ST segment taken from the V standard lead.Research  results.  Significant  differences  were  found  between  inter-parametric  connections  of  ST  segment amplitude and JT interval duration at the pre and post-training testing. Observed changes at different hierarchical levels of the body systems revealed inadequate cardiac metabolic processes, leading to changes in the metabolic rate of the myocardium and reflected in the dynamics of all investigated interactions.Discussion and conclusions. It has been found that peculiarities of the interactions of ECG indices interactions show the exposure of the  functional changes in the body at the onset of the workload. The alterations of the functional state of the body and the signs of fatigue, after athletes performed two high intensity training sessions per day, can be assessed using the approach of the evaluation of interactions between functional variables. Therefore the evaluation of the interactions of physiological signals by using time series analysis methods is suitable for the observation of these processes and the functional state of the body.Keywords: electrocardiogram, time series, functional state.

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