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Tsitouras C.,TEI of Chalkis | Famelis I.T.,Technological Educational Institute of Athens | Simos T.E.,King Saud University | Simos T.E.,University of Peloponnese
Computers and Mathematics with Applications | Year: 2011

Modified RungeKutta (mRK) methods can have interesting properties as their coefficients may depend on the step length. By a simple perturbation of very few coefficients we may produce various function-fitted methods and avoid the overload of evaluating all the coefficients in every step. It is known that, for RungeKutta methods, each order condition corresponds to a rooted tree. When we expand this theory to the case of mRK methods, some of the rooted trees produce additional trees, called mRK rooted trees, and so additional conditions of order. In this work we present the relative theory including a theorem for the generating function of these additional mRK trees and explain the procedure to determine the extra algebraic equations of condition generated for a major subcategory of these methods. Moreover, efficient symbolic codes are provided for the enumeration of the trees and the generation of the additional order conditions. Finally, phase-lag and phase-fitted properties are analyzed for this case and specific phase-fitted pairs of orders 8(6) and 6(5) are presented and tested. © 2011 Elsevier Ltd. All rights reserved.

Tsitouras C.,TEI of Chalkis
Computers and Mathematics with Applications | Year: 2011

Among the most popular methods for the solution of the Initial Value Problem are the Runge-Kutta pairs of orders 5 and 4. These methods can be derived solving a system of nonlinear equations for its coefficients. To achieve this, we usually admit various simplifying assumptions. The most common of them are the so-called row simplifying assumptions. Here we neglect them and present an algorithm for the construction of Runge-Kutta pairs of orders 5 and 4 based only in the first column simplifying assumption. The result is a pair that outperforms other known pairs in the bibliography when tested to the standard set of problems of DETEST. A cost free fourth order formula is also derived for handling dense output. © 2011 Elsevier Ltd. All rights reserved.

Marinagi C.,TEI of Chalkis | Skourlas C.,Technological Educational Institute of Athens
Proceedings of the IADIS International Conference Mobile Learning 2012, ML 2012 | Year: 2012

This paper presents a wireless distributed architecture for Personalized Educational Learning Environments - PELE used for supporting students with disabilities and learning difficulties and the collaboration of these environments. The architecture aims at enabling accessibility for Deaf (D) and Hard-of-Hearing (HH) students as well as dyslexic students. Devices that support mobile learning, such as Personal Digital Assistants (PDAs) are integrated in educational scenarios to support educational activities, such as giving lectures in the mainstream class, attending classes, or working in the laboratory, participating in assessments and participating in exams. We present and discuss how wireless networks, personalization techniques, and mobile learning form an attractive and helpful framework for supporting specific categories of students with disabilities and learning difficulties. Some utilization scenarios (use cases) are also given to demonstrate the various types of teaching and personalized services provided by the architecture. © 2012 IADIS.

Tsitouras Ch.,TEI of Chalkis | Famelis I.T.,Technological Educational Institute of Athens
New Astronomy | Year: 2012

In this paper we present Runge-Kutta-Nyström (RKN) pairs of orders 4(3) and 6(4). We choose a test orbit from the Kepler problem to integrate for a specific tolerance. Then we train the free parameters of the above RKN4(3) and RKN6(4) families to perform optimally. For that we form a neural network approach and minimize its objective function using a differential evolution optimization technique. Finally we observe that the produced pairs outperform standard pairs from the literature for Pleiades orbits and Kepler problem over a wide range of eccentricities and tolerances. © 2011 Elsevier B.V. All rights reserved.

Massouros Ch.G.,TEI of Chalkis | Massouros G.G.,Klious st.
AIP Conference Proceedings | Year: 2010

In the hypecompositional structures, unlike the classical ones, there exist several types of identities. This paper deals with two main types of identities, the scalar and strong ones and with the hypergroups in which they appear. Certain such hypergroups e.g. the fortified join hypergroup and the join polysymmetric hypergroup derived from the theory of formal languages and automata. © 2010 American Institute of Physics.

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