MATHEMATICAL MODELLING AND ANALYSIS

Transcription

1 ISSN MATHEMATICAL MODELLING AND ANALYSIS THE BALTIC JOURNAL ON MATHEMATICAL APPLICATIONS, NUMERICAL ANALYSIS AND DIFFERENTIAL EQUATIONS Volume 9 Number Electronical edition available at Abstracted/Indexed in: Mathematical Reviews Zentralblatt für Mathematik Referativnyi Zhurnal(VINITI information publication) 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 Volume 9 Number Electronical edition available at Vilnius Technika 2004

3 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 G. Erbacci (Italy) Supercomputing Group - InterUniversity Computing Center erbacci@cineca.it A. Fitt (UK) University of Southampton adf@maths.soton.ac.uk V. Gromak (Belarus) Belarussian State Univ., Minsk grom@bsu.by O. Iliev (Germany) Institute for Industrial Mathematics, Kaiserslautern iliev@itwm.uni-kl.de F. Ivanauskas (Lithuania) Vilnius University Feliksas.Ivanauskas@mif.vu.lt J. Janno (Estonia) Tallinn Technical University janno@ioc.ee H. Kalis (Latvia) Institute of Mathematics of LAS and UL, Riga kalis@latnet.lv V. Korzyuk (Belarus) Belarussian State Univ., Minsk Korzyuk@org.bsu.unibel.by A. Krylovas (Lithuania) Vilnius Gediminas Technical University akr@fm.vtu.lt Ü. Lepik (Estonia) University of Tartu ylepik@math.ut.ee P. Matus (Belarus) Institute of Mathematics, Minsk matus@im.bas-net.by M. Meilūnas (Lithuania) Vilnius Gediminas Technical University mm@fm.vtu.lt H. Ockendon (UK) Oxford Centre for Industrial and Applied Mathematics ockendon@maths.ox.ac.uk W. Okrasinski (Poland) University of Zielona Gora W.Okrasinski@im.uz.zgora.pl A. Pedas (Estonia) University of Tartu arvet.pedas@ut.ee K. Pileckas (Lithuania) Institute of Mathematics and Informatics pileckas@ktl.mii.lt U. Raitums (Latvia) Institute of Mathematics of LAS and UL, Riga uldis.raitums@mii.lu.lv A. Reinfelds (Latvia) Institute of Mathematics of LAS and UL, Riga reinf@latnet.lv J. Rokicki (Poland) Institute of Aeronautics, Warsaw jack@meil.pw.edu.pl S. Rutkauskas (Lithuania) Institute of Mathematics and Informatics, Vilnius stasysr@ktl.mii.lt M. Sapagovas (Lithuania) Institute of Mathematics and Informatics, Vilnius M.Sapagovas@ktl.mii.lt E. Tamme (Estonia) University of Tartu enn_t@ut.ee P. Vabishchevich (Russia) Institute for Mathematical Modelling, Moscow vab@ibrae.ac.ru G. Vainikko (Estonia) Estonian Academy of Sciences gen@ut.ee M. Weber (Germany) Technische Universität Dresden weber@math.tu-dresden.de G. Yelenin (Russia) M.V. Lomonosov Moscow State University yelenin@orc.ru A. Zemitis (Latvija) Ventspils University College zemitis@venta.lv A. Zlotnik (Russia) Power Engineering Institute, Moscow zlotnik@apmsun.mpei.ac.ru c Vilnius Gediminas Technical University, 2004

4 Authors Index Mathematical Modelling and Analysis, Volume 9, 2004 Avenhaus R.: Applications of Inspection Games Batrakov K.: Modelling of Quasi- Cherenkov Electron Beam Instability in Periodical Structures... 1 Bolotin I.B.: The First Basic Boundary Value Problem of Riemann s Type for Bianalytical Functions in a Plane with Slots Bolotin I.B.: The Second Boundary Value Problem of Riemann s Type for Bianalytical Functions with Discontinuous Coefficients193 Cēbers A.: see Cīrulis T Chakravarty S.: Numerical Simulation of Unsteady Two- Layered Pulsatile Blood Flow in a Stenosed Flexible Artery: Effect of Peripheral Layer Viscosity99 Chtcheritsa O.V.: Implicit Numerical Algorithm for the Solution of Phase Transition Problems in Multi-Component Alloys Čiegis R.: see Krylovas A Čiegis R.: Parallel Numerical Modelling of Short Laser Pulse Compression Čiegis R.: Mathematical Modelling of Water Flow in Paper Press Machines Cīrulis T.: Comparative Analysis by Means of Finite Differences and DM Methods for Linearized Problem of Gyrotrons Cīrulis T.: Dynamics of small Bubble Interface Perturbations in Vertical Hele-Shaw Cell with Magnetic Liquid under the Action of Normal Magnetic Field Dement ev A.: see Čiegis R Denisovas V.: see Švitra D Dhar J.: Diffusion of Population under the Influence Industrialization in a Twin-City Environment Dubatovskaya M.: On an Exact Description of the Schottky Groups of Symmetries137 Dumbrajs O.: Numerical Solution of Single Mode Gyrotron Equation Essoufi El-H.: see Sofonea M..229 Garška R.: Spatial Analysis and Prediction of Curonian Lagoon Data with Gstat 39 Gromyko G.: On the Cooling of a Free Thin Film at the Presence of the van der Waals Forces J. Dhar: A Prey-predator Model with Diffusion and a Supplementary Resource for the Prey in a Two-Patch Environment...9 Juščenko N.: see Švitra D Kalis H.: see Cīrulis T Kalis H.: see Dumbrajs O Krūminienė I.: see Garška R... 39

5 ii Editor-in-Chief R. Čiegis Krylovas A.: A Review of Numerical Asymptotic Averaging for Weakly Nonlinear Hyperbolic Waves Lietuvietis O.: see Cīrulis T.. 127, 287 Mandal A.: see Chakravarty S..99 Mandal P.K.: see Chakravarty S. 99 Mazhorova O.S.: see Chtcheritsa O.V Meilūnas M.: see Čiegis R Misevičius A.: An Improved Hybrid Optimization Algorithm for the Quadratic Assignment Problem.149 Omrani K.: On Fully Discrete Galerkin Approximations for the Cahn-Hilliard Equation 313 Popov Yu.P.: see Chtcheritsa O.V. 253 Popova L.: see Gromyko G Radžiūnas M.: see Sieber J...51 Rasulov K.M.: About the Solution in Closed Form of Generalized Markushevich Boundary Value Problem in the Class of Analytical Functions Rasulov K.M.: see Bolotin I.B.. 91 Reinfelds A.: see Dumbrajs O.. 25 Rogosin S.: see Dubatovskaya M. 137 Rybak I.V.: Monotone and Conservative Difference Schemes for Elliptic Equations with Mixed Derivatives Schneider K.R.: see Sieber J Sieber J.: Dynamics of Multisection Semiconductor Lasers 51 Šilko G.: see Čiegis R Singh H.:see Dhar J Socolowsky J.: On the Existence and Uniqueness of Two- Fluid Channel Flows.. 67 Sofonea M.: A Piezoelectric Contact Problem with Slip Dependent Coefficient of Friction Štikonas A.: see Čiegis R Švitra D.: Computer Modelling of Density Dynamics of Single- Species Laboratory Insects Population Sytova S.: see Batrakov K...1 Tabakova S.: see Gromyko G Tammeraid I.: Generalized Riesz Method and Convergence Acceleration Tarang I.: Stability of the Spline Collocation Method for Second Order Volterra Integro-Differential Equations 79 Zyuzina E.L.: Stability of Three- Level Difference Schemes with Respect to the Right- Hand Side

6 Mathematical Modelling and Analysis, Volume 9 Number 4, 2004 a Second Announcement 10th International Conference Mathematical Modelling and Analysis and 2nd International Conference Computational Methods in Applied Mathematics June 1 5, 2005, Trakai, Lithuania Conference organizers: The International Association for Mathematics and Computers in Simulation (IMACS), the European Consortium for Mathematics in Industry (ECMI), Vilnius Gediminas Technical University, Institute of Mathematics and Informatics, Vilnius University and Computational Methods in Applied Mathematics (CMAM). 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. Meilūnas (Lithuania), H. Neunzert (Germany), A. Pedas (Estonia), U. Raitums (Latvia), A. Reinfelds (Latvia), J. Rokicki (Poland), M. Sapagovas (Lithuania), I. Sloan (Australia), P. Vabishchevich (Russia), G. Vainikko (Estonia), A. Zemitis (Latvia) 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 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; 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), Invited Semiplenary lectures (30 min) and Contributed Talks (20 min). The program also includes Poster Sessions.

7 b Editor-in-Chief R. Čiegis We also invite participants to organize mini-symposia. The format for a minisymposium is a principal lecture (30 min) and a number of communications of 20 minutes given by the other speakers. The mini-symposia will be scheduled in parallel sessions. The deadline for proposals of mini-symposia is January 30, The following mini-symposia are approved: 1. "Modelling and simulation of hydrogeological and geo-environmental problems", co-organizers: H. Neunzert, O. Iliev (ITWM, Kaiserslautern, Germany), P.Vabishchevich (Moscow university, Russia), neunzert,iliev@itwm.fhg.de 2. "Navier - Stokes equations and Computational Fluid Dynamics", coorganizers: W.Zajaczkowski, J. Rokicki (Poland), K. Pileckas (IMI, Vilnius, Lithuania) W.Zajaczkowski@impan.gov.pl, jack@meil.pw.edu.pl, pileckas@ktl.mii.lt 3. "Computational Mechanics", organizers: R. Belevicius (VGTU, Vilnius, Lithuania), rb@fm.vtu.lt 4. "Parallel and grid computing: algorithms and applications", co-organizers: M. Sosonkina (Ames Laboratory and Iowa State University, USA), R. Ciegis (VGTU, Vilnius, Lithuania), rc@fm.vtu.lt 5. "Mathematical models including non-local boundary conditions", co-organizers: M. Sapagovas (IMI, Vilnius, Lithuania), V.L. Makarov (Kiev, Ukraine), m.sapagovas@ktl.mii.lt Abstracts and Proceeding. Authors are requested to send an abstract (1 page) before March 30, Instructions and a style file for the preparation of the abstracts are available athttp:// Conference materials. The selected papers of the Conference will be published in Vol. 10 of "Mathematical Modelling and Analysis" and in Vol. 5 of Journal "Computational Methods in Applied Mathematics" All papers will be peer-reviewed. Registration. For registration please fill in the registration form at our web-site. Please inform us about your arrival and departure dates. The registration fee is 240 EUR and can be paid directly at the registration desk. It includes the abstract volume, all local expenses (accommodation in two bed rooms for four nights and three meals per day), conference dinner and coffee breaks. Persons who wish accommodation in single rooms should pay the registration fee 300 EUR. The fee for accompanying persons is 140 EUR. It icludes the reception, conference dinner, social events and accommodation in two bed rooms for four nights and three meals per day. Full traveling and registration information will be given on our web-site. Deadlines. Abstracts: March 30, 2005; Notification of participation and reservation of accommodation: May 10, 2005 Correspondence address. Dr. A. Štikonas (MMA2005 & CMAM2), Institute of Mathematics and Informatics, Akademijos 4, LT-08663, Vilnius, Lithuania. Ph.: (+370) , (+370) , Fax: (+370) Questions regarding MMA2005 & CMAM2 should be addressed to mma@konf.vtu.lt

8 Mathematical Modelling and Analysis, Volume 9 Number 4, 2004 c INFORMATION FOR AUTHORS Aims and Scope MATHEMATICAL MODELLING AND ANALYSIS 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 EPS format. The list of references should always be in alphabetical order. We ask to submit your references writen with BibTEX. The complete reference should be listed as follows.

9 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), 3 40, We ask to submit your papers written in L A TEX 2ε. You may obtain the MATHEMATICAL MODELLING AND ANALYSIS style files from our ftp server (ftp://inga.vtu.lt/mma/journal/). We supply a style file mma.cls and a L A TEX 2ε template filetemplate.tex andplain_mma.bst 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 mma@fm.vtu.lt Internet Address Information about journal MATHEMATICAL MODELLING AND ANALYSIS the Baltic Journal on Mathematical Applications, Numerical Analysis and Differential Equations and online edition of all papers are presented on Internet:

10 Mathematical Modelling and Analysis The Baltic Journal on Mathematical Applications, Numerical Analysis and Differential Equations Editor-in-Chief R. Čiegis Volume 9, Number 4, Matematinis modeliavimas ir analizė Vyriausiasis redaktorius R. Čiegis Tomas 9, Numeris 4, 2004 SL ,5 apsk. leid. l. Tiražas 200 egz. Leido Vilniaus Gedimino technikos universiteto leidykla Technika, Saulėtekio al. 11, LT Vilnius-40 Spausdino UAB Sapnų sala, S. Moniuškos g , LT Vilnius

11 Mathematical Modelling and Analysis Volume 9, Number 4, 2004 CONTENTS O.V. Chtcheritsa, O.S. Mazhorova, Yu.P. Popov Implicit Numerical Algorithm for the Solution of Phase Transition Problems in Multi-Component Alloys R. Čiegis, M. Meilûnas, A. Štikonas Mathematical Modelling of Water Flow in Paper Press Machines T. Cīrulis, O. Lietuvietis, A.Cēbers Dynamics of small Bubble Interface Perturbations in Vertical Hele- Shaw Cell with Magnetic Liquid under the Action of Normal Magnetic Field G. Gromyko, S. Tabakova, L. Popova On the Cooling of a Free Thin Film at the Presence of the van der Waals Forces K. Omrani On Fully Discrete Galerkin Approximations for the Cahn-Hilliard Equation D. Švitra, V. Denisovas, N. Juščenko Computer Modelling of Density Dynamics of Single-Species Laboratory Insects Population I. Tammeraid Generalized Riesz Method and Convergence Acceleration