E. Miletics

8872953500

Publications - 5

A mathematical model for the middle ear ventilation

G. Molnárka M. Fücsek E. Miletics

Publication Name: Aip Conference Proceedings

Publication Date: 2008-10-22

Volume: 1046

Issue: Unknown

Page Range: 106-109

Description:

The otitis media is one of the mostly existing illness for the children, therefore investigation of the human middle ear ventilation is an actual problem. In earlier investigations both experimental and theoretical approach one can find in ([1]-[3]). Here we give a new mathematical and computer model to simulate this ventilation process. This model able to describe the diffusion and flow processes simultaneously, therefore it gives more precise results than earlier models did. The article contains the mathematical model and some results of the simulation. © 2008 American Institute of Physics.

Open Access: Yes

DOI: 10.1063/1.2997288

Implicit extension of Taylor series method with numerical derivatives for initial value problems

G. Molnárka E. Miletics

Publication Name: Computers and Mathematics with Applications

Publication Date: 2005-10-01

Volume: 50

Issue: 7

Page Range: 1167-1177

Description:

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of this algorithms is based on the approximate calculation of higher derivatives using well-known finite-difference technique for the partial differential equations. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval integration. This property offers different facility for adaptive error control. This paper describes several explicit Taylor series algorithms with numerical derivatives and their implicit extension and examines its consistency and stability properties. The implicit extension based on a collocation term added to the explicit truncated Taylor series and the approximate solution obtained as a continuously differentiable piecewise polynomials function. Some numerical test results is presented to prove the efficiency of these new-old algorithm. © 2005 Elsevier Ltd. All rights reserved.

Open Access: Yes

DOI: 10.1016/j.camwa.2005.08.017

Energy conservative algorithm for numerical solution of ODEs initial value problems

E. Miletics

Publication Name: Journal of Computational Methods in Sciences and Engineering

Publication Date: 2005-01-01

Volume: 5

Issue: 1

Page Range: 39-45

Description:

The numerical treatment of the ODE initial value problems is an intensively researched field. Recently the qualitative algorithms, such as monotonicity and positivity preserving algorithms are in the focus of investigation. For the dynamical systems the energy conservative algorithms are very important. In the case of Hamiltonian system the symplectic algorithms are very effective. This kind of algorithm is not adaptive, but doubtless they are powerful. The high-efficiency computers and the computer algebraic software systems allow us to create efficient adaptive energy conservative numerical algorithm for solving ODE initial value problems. In this article an adaptive numerical-analytical algorithm is suggested which very effectively can be applied for Hamiltonian systems, but the idea of construction can be adaptable for other initial value problems too, where there are some quantity preserved in time. The idea and the efficiency of the proposed algorithm will be presented by simple examples, such as the Lotka-Volterra and linear oscillator problems.

Open Access: Yes

DOI: 10.3233/jcm-2005-5104

Energy-Conservative Algorithm for the Numerical Solution of Initial-Value Hamiltonian System Problems

E. Miletics

Publication Name: Journal of Advanced Computational Intelligence and Intelligent Informatics

Publication Date: 2004-09-01

Volume: 8

Issue: 5

Page Range: 495-498

Description:

The numerical treatment of ODE initial-value problems has been intensively researched. Energy-conservative algorithms are very important to dinamic systems. For the Hamiltonian system the symplectic algorithms are very effective. Powerful computers and algebraic software enable the creation of efficient numerical algorithms for solving ODE initial-value problems. In this paper, we propose an adaptive energy-conservative numerical-analytical algorithm for Hamiltonian systems. This algorithm is adaptable to initial-value problems where some quantities are preserved. The algorithm and its efficiency are presented for solving two-body and linear oscillator problems.

Open Access: Yes

DOI: 10.20965/jaciii.2004.p0495

Taylor series method with numerical derivatives for initial value problems

G. Molnárka E. Miletics

Publication Name: Journal of Computational Methods in Sciences and Engineering

Publication Date: 2004-01-01

Volume: 4

Issue: 1-2

Page Range: 105-114

Description:

The Taylor series method is one of the earliest analytic-numeric algorithms for approximate solution of initial value problems for ordinary differential equations. The main idea of the rehabilitation of these algorithms is based on the approximate calculation of higher derivatives using well-known technique for the partial differential equations. In some cases such algorithms will be much more complicated than a R-K methods, because it will require more function evaluation than well-known classical algorithms. However these evaluations can be accomplished fully parallel and the coefficients of truncated Taylor series can be calculated with matrix-vector operations. For large systems these operations suit for the parallel computers. The approximate solution is given as a piecewise polynomial function defined on the subintervals of the whole interval and the local error of this solution at the interior points of the subinterval is less than that one at the end point. This property offers different facility for adaptive error control. This paper describes several above-mentioned algorithms and examines its consistency and stability properties. It demonstrates some numerical test results for stiff systems herewith we attempt to prove the efficiency of these new-old algorithms.

Open Access: Yes

DOI: 10.3233/jcm-2004-41-213