scholarly journals Evolutionary Derivation of Runge–Kutta Pairs of Orders 5(4) Specially Tuned for Problems with Periodic Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2306
Author(s):  
Vladislav N. Kovalnogov ◽  
Ruslan V. Fedorov ◽  
Andrey V. Chukalin ◽  
Theodore E. Simos ◽  
Charalampos Tsitouras
Keyword(s):  
Periodic Solutions ◽  
State Of The Art ◽  
Relevant Literature ◽  
Special Property ◽  
Phase Lag ◽  
The Family ◽  
Standard Set ◽  
Free Parameters ◽  
Runge Kutta ◽  
High Phase

The purpose of the present work is to construct a new Runge–Kutta pair of orders five and four to outperform the state-of-the-art in these kind of methods when addressing problems with periodic solutions. We consider the family of such pairs that the celebrated Dormand–Prince pair also belongs. The chosen family comes with coefficients that all depend on five free parameters. These latter parameters are tuned in a way to furnish a new method that performs best on a couple of oscillators. Then, we observe that this trained pair outperforms other well known methods in the relevant literature in a standard set of problems with periodic solutions. This is remarkable since no special property holds such as high phase-lag order or an extended interval of periodicity.

High Phase-Lag-Order Runge--Kutta and Nyström Pairs

1999 ◽  
Vol 21 (2) ◽  
pp. 747-763 ◽  
Author(s):  
S. N. Papakostas ◽  
Ch. Tsitouras
Keyword(s):  
Phase Lag ◽  
Runge Kutta ◽  
High Phase

High phase-lag order Runge Kutta pairs of orders 8(7)

2017 ◽  
Author(s):  
Ch. Tsitouras ◽  
Ioannis Th. Famelis
Keyword(s):  
Phase Lag ◽  
Runge Kutta ◽  
High Phase

scholarly journals Runge–Kutta Pairs of Orders 5(4) Trained to Best Address Keplerian Type Orbits

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2400
Author(s):  
Vladislav N. Kovalnogov ◽  
Ruslan V. Fedorov ◽  
Tamara V. Karpukhina ◽  
Theodore E. Simos ◽  
Charalampos Tsitouras
Keyword(s):  
Differential Evolution ◽  
Nonlinear Equations ◽  
Function Evaluation ◽  
The Family ◽  
Last Stage ◽  
Free Parameters ◽  
Runge Kutta

The derivation of Runge–Kutta pairs of orders five and four that effectively uses six stages per step is considered. The coefficients provided by such a method are 27 and have to satisfy a system of 25 nonlinear equations. Traditionally, various solutions have been tried. Each of these solutions makes use of some simplified assumptions and offers different families of methods. Here, we make use of the most celebrated family to appear in the literature, where we may use as the last stage the first function evaluation from the next step (FSAL property). The family under consideration has the advantage of being solved explicitly. Actually, we arrive at a subsystem where all the coefficients are found with respect to five free parameters. These free parameters are adjusted (trained) in order to deliver a pair that outperforms other similar pairs of orders 5(4) in Keplerian type orbits, e.g., Kepler, perturbed Kepler, Arenstorf orbit or Pleiades. The training uses differential evolution technique. The finally proposed pair has a remarkable performance and offers on average more than a digit of accuracy in a variety of orbits.

scholarly journals Social Media Adoption, Usage And Impact In Business-To-Business (B2B) Context: A State-Of-The-Art Literature Review

2021 ◽  
Author(s):  
Yogesh K. Dwivedi ◽  
Elvira Ismagilova ◽  
Nripendra P. Rana ◽  
Ramakrishnan Raman
Keyword(s):  
Social Media ◽  
Media Use ◽  
State Of The Art ◽  
Relevant Literature ◽  
Comprehensive Analysis ◽  
Social Media Use ◽  
Weight Analysis ◽  
Social Media Tools ◽  
Use Of Social Media ◽  
Business To Business

AbstractSocial media plays an important part in the digital transformation of businesses. This research provides a comprehensive analysis of the use of social media by business-to-business (B2B) companies. The current study focuses on the number of aspects of social media such as the effect of social media, social media tools, social media use, adoption of social media use and its barriers, social media strategies, and measuring the effectiveness of use of social media. This research provides a valuable synthesis of the relevant literature on social media in B2B context by analysing, performing weight analysis and discussing the key findings from existing research on social media. The findings of this study can be used as an informative framework on social media for both, academic and practitioners.

Information processing by elderly consumers: a five-decade review

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Gianluigi Guido ◽  
Marco Pichierri ◽  
Cristian Rizzo ◽  
Verdiana Chieffi ◽  
George Moschis
Keyword(s):  
Information Processing ◽  
Design Methodology ◽  
State Of The Art ◽  
Relevant Literature ◽  
Academic Research ◽  
The Elderly ◽  
Marketing Strategies ◽  
Content Type ◽  
Processing Activity ◽  
Elderly Consumers

Purpose The purpose of this study is to review scholarly research on elderly consumers’ information processing and suggest implications for services marketing. Design/methodology/approach The review encompasses a five-decade period (1970–2018) of academic research and presents relevant literature in four main areas related to information processing: sensation, attention, interpretation and memory. Findings The study illustrates how each of the aforementioned phases of the information processing activity may affect how elderly individuals buy and consume products and services, emphasizing the need for a better comprehension of the elderly to develop effectual marketing strategies. Originality/value The study provides readers with detailed state-of-the-art knowledge about older consumers’ information processing, offering a comprehensive review of academic research that companies can use to improve the effectiveness of their marketing efforts that target the elderly market.

Reliability Analysis of Great Lakes Marine Diesels: State of the Art and Current Modeling

1990 ◽  
Vol 27 (04) ◽  
pp. 237-249
Author(s):  
Anastassios N. Perakis ◽  
Bahadir Inozu
Keyword(s):  
Great Lakes ◽  
Diesel Engines ◽  
Failure Modes ◽  
State Of The Art ◽  
Relevant Literature ◽  
Fault Tree Analysis ◽  
Reliability Engineering ◽  
Marine Industry ◽  
Marine Diesel ◽  
Basic Concepts

Some essential steps for the application of reliability, availability, and maintainability (RAM) techniques to marine diesel engines are presented. The paper begins with a summary of the basic concepts of reliability engineering, followed by a survey of the relevant literature on RAM applications to the marine industry and to marine diesel engines in particular. Next, the results of an informal survey of the reliability, maintenance, and replacement practices of Great Lakes operators are presented. Finally, the first two steps for a RAM application, failure modes and effects analysis and fault tree analysis, are introduced and applied for a prototype Colt-Pielstick marine diesel engine.

On the authorship and publication dates of Theraphosa and Theraphosidae (Araneae, Mygalomorphae): a clarification

Bionomina ◽  
2021 ◽  
Vol 24 (1) ◽  
Author(s):  
RAINER BREITLING
Keyword(s):  
19Th Century ◽  
Relevant Literature ◽  
Historical Context ◽  
Publication Date ◽  
Diverse Group ◽  
Early 19Th Century ◽  
The Family ◽  
Minority View ◽  
Case Based ◽  
Selection Of

The genus Theraphosa was established by Thorell (1870) as the type genus of the simultaneously published family Theraphosidae, the most diverse group of mygalomorph spiders. This authorship and publication date have long been accepted by the majority of authors. However, there has been a long-standing minority view that the genus name should be attributed to Walckenaer (1805), and the publication date of the family name changed to 1869.             A thought-provoking recent publication has examined this case. Based on a limited selection of the relevant literature, the authors struggled to make sense of their sources and prematurely concluded that the minority opinion might indeed be correct. They overlooked the potentially destabilising implications of this reattribution.             This paper revisits the evidence in the light of a much wider range of relevant publications, places it in its important historical context and, on the basis of the current rules of nomenclature, concludes that the traditional consensus has indeed been correct.                 Thus, Theraphosa Thorell, 1870 is the type genus of Theraphosidae Thorell, 1870 and a nomen protectum, while Theraphosa Schinz, 1823 is a nomen oblitum, mostly limited to the German textbook literature of the early 19th century. Teraphosa Eichwald, 1830 and Teraphosa Gistel, 1848 are junior synonyms of Avicularia Lamarck, 1818 (syn. nov.). Theraphosa Walckenaer, 1805 is a suprageneric name of the class-series (synonymous to Mygalomorphae) and not available at the genus level.

State of the Art — 1973

1973 ◽  
Vol 18 (3) ◽  
pp. 175-183 ◽  
Author(s):  
Nathan B. Epstein ◽  
Duane S. Bishop
Keyword(s):  
State Of The Art ◽  
Therapeutic Process ◽  
Scientific Discipline ◽  
Therapeutic Approaches ◽  
Training And Education ◽  
Rigorous Approach ◽  
The Family ◽  
Process And Outcome ◽  
Scientific Approach ◽  
Made In

In summary, it can be said that progress is being made in the field, but slowly. The ‘art’ is vigorous, vital and exciting. The ranks of family therapists are swelling and they are coming from backgrounds of different theoretical persuasions and with varying degrees of sophistication in their training and education. This mélange does lead to excitement and turbulence but often detracts from the necessary rigour that a scientific discipline must develop in order to reach maturity. Systems theory allows for easy conceptualization of one another's behaviour in the system, and permits a much clearer understanding of the therapeutic process based upon it, in contrast to therapeutic approaches based on other models. The authors found negotiation to be therapeutically effective when made explicit. In addition they place the focus on the ‘here and now’ and encourage the increased labeling by family members of interactions (affective and behavioural) and their effects (affective and behavioural), according to the Family Categories Schema previously referred to. Efforts are directed especially towards dealing with the current resistances to problem solutions. Epstein et al. have reported on an ongoing program of research which attempts to examine the process and outcome of family therapy (7,10,21,22,25,26). What is needed now is a more rigorous approach to research and the development of a necessary theoretical base in order that a more systematic and scientific approach can be developed for treating families.

scholarly journals Eighth Order Two-Step Methods Trained to Perform Better on Keplerian-Type Orbits

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3071
Author(s):  
Vladislav N. Kovalnogov ◽  
Ruslan V. Fedorov ◽  
Andrey V. Chukalin ◽  
Theodore E. Simos ◽  
Charalampos Tsitouras
Keyword(s):  
Differential Evolution ◽  
Eighth Order ◽  
Numerical Tests ◽  
Wide Range ◽  
The Family ◽  
Free Parameters

The family of Numerov-type methods that effectively uses seven stages per step is considered. All the coefficients of the methods belonging to this family can be expressed analytically with respect to four free parameters. These coefficients are trained through a differential evolution technique in order to perform best in a wide range of Keplerian-type orbits. Then it is observed with extended numerical tests that a certain method behaves extremely well in a variety of orbits (e.g., Kepler, perturbed Kepler, Arenstorf, Pleiades) for various steplengths used by the methods and for various intervals of integration.

scholarly journals THE DETERMINANTS OF HOUSEHOLD SAVINGS IN POLAND

2017 ◽  
Vol 16 (2) ◽  
pp. 117-125 ◽  
Author(s):  
Tomasz Szopiński
Keyword(s):  
Household Income ◽  
Relevant Literature ◽  
Panel Study ◽  
Household Savings ◽  
Place Of Residence ◽  
The Family ◽  
Statistical Relationships

The relevant literature provides an array of factors determining the propensity of households to save. There is no unanimity among researchers as to the direction of statistical relationships among some variables such as, e.g. household income, the place of residence or concerns regarding the worsening of financial circumstances, and a household’s propensity to save. The aim of this article is to verify the statistical relationships between the amount of savings of Polish households and their attributes, such as: income, biological type of the family, and the size of the place of residence. The author of the article analyses the responses provided by Polish households with regard to the size of their savings measured as a multiple of their income. The data under analysis were collected during a panel study Diagnoza społeczna 2015 (ang. Social Diagnosis 2015). Higher earnings were accompanied by higher levels of savings. It was more common for households from bigger cities to have higher earnings. Taking into consideration the biological type of the family, childless marriages and people, who lived alone, declared having the highest savings.

Sign in / Sign up

Export Citation Format

Share Document