MATHEMATICAL MODELLING AND ANALYSIS

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1 9 ISSN MATHEMATICAL MODELLING AND ANALYSIS THE BALTIC JOURNAL ON MATHEMATICAL APPLICATIONS NUMERICAL ANALYSIS AND DIFFERENTIAL EQUATIONS Volume 9 Number Electronical edition available at << : ;<1= :? < Abstracted/Indexed in: 7 < 67 < 7? ; < 7? #?17 <1< 9 7 < 67 < 7 < ; = 7?!"#"%$"& 9' 67 < ' = #? 7 <(' *) Vilnius Technika 2004

2 ISSN Institute of Mathematics Latvian Academy of Sciences University of Latvia Institute of Mathematics and Informatics Vilnius University of Tartu Vilnius Gediminas Technical University MATHEMATICAL MODELLING AND ANALYSIS THE BALTIC JOURNAL ON MATHEMATICAL APPLICATIONS NUMERICAL ANALYSIS AND DIFFERENTIAL EQUATIONS Electronical edition available at << >:;<1= :? < ( Vilnius Technika 2004

3 C Editor-in-Chief R. Čiegis Vilnius Gediminas Technical University Saulėtekio al. 11 LT Vilnius Lithuania Executive Editor A. Štikonas Institute of Mathematics and Informatics Akademijos 4 LT Vilnius Lithuania International Editorial Board! " # $ V. Abrashin (Belarus) Institute of Mathematics Minsk A. Buikis (Latvia) Institute of Mathematics of LAS and UL Riga A. Fitt (UK) University of Southampton V. Gromak (Belarus) Belarussian State Univ. Minsk O. Iliev (Germany) Institute for Industrial Mathematics Kaiserslautern " 1!%-) (" ( ) * ++ ) % &% " # ' +& & "/ 0$ "% 3 *4% 5 # ' F. Ivanauskas (Lithuania) Vilnius University J. Janno (Estonia) Tallinn Technical University "" H. Kalis (Latvia) Institute of Mathematics of LAS and UL Riga V. Korzyuk (Belarus) Belarussian State Univ. Minsk + 8$% + A. Krylovas (Lithuania) Vilnius Gediminas Technical University Ü. Lepik (Estonia) University of Tartu $ ":-% # "" P. Matus (Belarus) Institute of Mathematics Minsk M. Meilūnas (Lithuania) Vilnius Gediminas Technical University H. Ockendon (UK) Oxford Centre for Industrial and Applied Mathematics + &% "(+ ) '+ <# ) % % ". 9 "/ $ % - 0!". $ = W. Okrasinski (Poland) University of Zielona Gora A. Pedas (Estonia) University of Tartu ". : " ( # "" K. Pileckas (Lithuania) Institute of Mathematics and Informatics U. Raitums (Latvia) Institute of Mathematics of LAS and UL Riga -( ) A 53 ' ' ; ' '> %-%? 8. ;8 A. Reinfelds (Latvia) Institute of Mathematics of LAS and UL Riga J. Rokicki (Poland) Institute of Aeronautics Warsaw 6 S. Rutkauskas (Lithuania) Institute of Mathematics and Informatics Vilnius $ %/ B 5) ' + / :- : " % A) ' " " # ' % & " / 0:19 " ( :- M. Sapagovas (Lithuania) Institute of Mathematics and Informatics Vilnius D : + A) ' "-E. " " E. Tamme (Estonia) University of Tartu P. Vabishchevich (Russia) Institute for Mathematical Modelling Moscow "# 3 G. Vainikko (Estonia) Estonian Academy of Sciences M. Weber (Germany) Technische Universität Dresden 1" " - 5!("(" ;(" G. Yelenin (Russia) M.V. Lomonosov Moscow State University A. Zemitis (Latvija) Ventspils University College A. Zlotnik (Russia) Power Engineering Institute Moscow 8 + % : :") 3 " ( ) ;&%%-+. 8" 5 " # ' $" "- + ) c Vilnius Gediminas Technical University 2004

4 Mathematical Modelling and Analysis Volume 9 Number a 10th International Conference Mathematical Modelling and Analysis and 2nd International Conference Computational Methods in Applied Mathematics June Trakai Lithuania "!#%$'&%($*))%+.--/ Conference organizers: The European Consortium for Mathematics in Industry (ECMI) Vilnius Gediminas Technical University Institute of Mathematics and Informatics Vilnius University and Journal Computational Methods in Applied Mathematics. Aims: The Conference focuses on various aspects of mathematical modelling and usage of finite difference and finite element methods for numerical solution of modern problems of science and engineering. It aims in particular at fostering cooperation among practitioners and theoreticians in this field. Another very important goal of the MMA and CMAM meetings is to assist the creation and maintenance of contacts between scientists from the West and the East. Working language of the Conference is English. The basic topics: Analysis of numerical methods for solving problems of mathematical physics; Parallel algorithms and parallel computing; Application of numerical methods to engineering problems; Analysis of ODE and PDE problems and applications; Navier - Stokes equations and Computational Fluid Dynamics; Image processing; Financial mathematics and mathematics in economics; Scientific computation. The scientific program includes invited plenary talks (40 min) and contributed talks (20 min). We also invite participants to organize minisymposiums. The format for a minisymposium might be a principal lecture and a number of communications of minutes given by the other speakers. The minisymposia will be scheduled in parallel sessions. International Organizing Committee R. Čiegis (Lithuania - Chairman) P. Matus (Belarus - Vice-chairman) A. Štikonas (Lithuania - Scientific secretary) R. Belevičius (Lithuania) A. Buikis (Latvia) I. Gaishun (Belarus) P. Hemker (Netherlands) O. Iliev (Germany) A. Iakubenia (Belarus) F. Ivanauskas (Lithuania) A. Krylovas (Lithuania) R. Lazarov (USA) M. Meil ūnas (Lithuania) H. Neunzert (Germany) A. Pedas (Estonia) U. Raitums (Latvia) A. Reinfelds (Latvia) J. Rokicki (Poland) M. Sapagovas (Lithuania) P. Vabishchevich (Russia) G. Vainikko (Estonia) A. Zemitis (Latvia)

5 b Editor-in-Chief R. Čiegis Abstracts and Proceedings Authors are requested to send an abstract (1 page) before March Instructions and a style file for the preparation of the abstracts are available at << : ;<1= :@? < 66#7 Conference materials The selected papers of the Conference will be published in Vol.10 of "Mathematical Modelling and Analysis" (The Baltic Journal on Mathematical Applications Numerical Analysis and Differential Equations) << : ;<1= :? < and in Vol.5 of Journal "Computational Methods in Applied Mathematics" << : : 9 ' All papers will be peer-reviewed. Correspondence address Dr. A. Štikonas (MMA2005 & CMAM2) Institute of Mathematics and Informatics Akademijos 4 LT-08663Vilnius Lithuania Ph.: (+370) (+370) Fax: (+370) Questions regarding MMA2005 & CMAM2 should be addressed to mma@konf.vtu.lt To receive the Second Announcement you must register at: << :;< = :@? < or to fill the registration form and send it by . Trakai is a popular center of tourism. It is situated 30 km from Vilnius. The town as well as its surroundings started developing in the XIII century as a state center. According to annals Grand Duke Gediminas after a successful hunt found a beautiful place not far from the then capital Kernave and decided to build a castle here. That is how a new castle was built in Senieji Trakai which at that time was called Trakai. The town of Trakai was first mentioned in German annals in 1337 which is regarded to be the official date of its foundation. When Grand Duke Gediminas finally settled in Vilnius Senieji Trakai was inherited by his son the Duke Kestutis. During the reign of Kestutis Naujieji Trakai was a place of intensive construction: one castle was built in the strait between lakes Galve and Lukos another one - on an island in lake Galve. A village grew around the castle. The distinctive feature of Trakai is that the town was built and preserved by people of different nationalities. Here lived communities of Karaites Tartars Lithuanians Russians and Polish. Both Christian and Karaites communities were granted separate self-government - Magdeburg - rights. The island castle was rebuilt in the second half of the XX century. In summer different festivals and concerts take place in the island castle. More information at http: :< 7 7 :? <

6 # " Mathematical Modelling and Analysis Volume 9 Number c INFORMATION FOR AUTHORS Aims and Scope & $ $" "# # the Baltic Journal on Mathematical Applications Numerical Analysis and Differential Equations publishes carefully selected papers of the high quality presenting new and important developments in all areas of mathematical modelling and analysis. The scope of the journal includes the following: All fields of Numerical analysis Mathematical aspects of Scientific Computing Parallel algorithms Mathematical modelling Analysis of ODE and PDE Approximation theory Optimization. Instructions for Authors Manuscript submitted to this journal will be considered for the publication with the understanding that the same work has not been published and is not under consideration for publication elswere. All the papers will be reviewed. Any manuscript which does not conform to the below instructions may be returned for the necessary revision. Papers submitted for publication should be written in English. The length of a paper is up to 20 pages. Each paper should have the following structure: the title the name(s) and institutional affiliation(s) of the author(s) the abstract (50-80 words) the text the list of references. All illustrations must be supplied on separate sheets and must be marked on the back with figure number title of paper and name of author. We welcome illustrations given in format. The list of references should always be in alphabetical order. We ask to submit your references writen with TEX. The complete reference should be listed as follows.

7 # " # " d References Editor-in-Chief R. Čiegis [1] A. Author. Article in proceedings. In: H. Ammann and V.A. Solonnikov(Eds.) Proc. of the 6th Intern. Conference NSEC-6 Palanga Lithuania 1997 Navier-Stokes Equations and Related Nonlinear Problems VSP/TEV Utrect/Vilnius [2] A. Author. Difference methods for initial value problems. Interscience Publishers New York (in Russian) [3] F. Author S. Author and T. Author. Article in journal. Journal 1(2) We ask to submit your papers written in L A TEX 2ε. You may obtain the & $ $" "# # style files from our ftp server (91< 7%:;<1=>:? < ' = 7? ). We supply a style file 61647%:? and a L A TEX 2ε template file < 6 #?17 < :< and #? : < file. Papers for publications (2 copies) should be send to: Editorial Office MATHEMATICAL MODELLING AND ANALYSIS The Baltic Journal on Mathematical Applications Numerical Analysis and Differential Equations Attn.: Dr. A. Štikonas Institute of Mathematics and Informatics Akademijos 4 LT Vilnius Lithuania Phone: (+370 5) Fax:(+370 5) You can send your papers by :;<1= :? < Internet Address Information about journal & $ $" "# # the Baltic Journal on Mathematical Applications Numerical Analysis and Differential Equations and online edition of all papers are presented on Internet: << : ;<1= :? < 6 647

8 Mathematical Modelling and Analysis The Baltic Journal on Mathematical Applications Numerical Analysis and Differential Equations Editor-in-Chief R. Čiegis Volume 9 Number << : ;<1= :@? < 66#7 Matematinis modeliavimas ir analizė Vyriausiasis redaktorius R. Čiegis Tomas 9 Numeris SL apsk. leid. l. Tiražas 150 egz. Leido Vilniaus Gedimino technikos universiteto leidykla Technika Saulėtekio al. 11 LT Vilnius-40 Spausdino UAB Sapnų sala S. Moniuškos g LT Vilnius

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MATHEMATICAL MODELLING AND ANALYSIS

ISSN 1392-6292 MATHEMATICAL MODELLING AND ANALYSIS THE BALTIC JOURNAL ON MATHEMATICAL APPLICATIONS, NUMERICAL ANALYSIS AND DIFFERENTIAL EQUATIONS Volume 9 Number 4 2004 Electronical edition available at