Table Of ContentIvan Dimov · István Faragó
Lubin Vulkov (Eds.)
6
8
3 Finite Difference Methods
1
1
S
C
N Theory and Applications
L
7th International Conference, FDM 2018
Lozenetz, Bulgaria, June 11–16, 2018
Revised Selected Papers
123
Lecture Notes in Computer Science 11386
Commenced Publication in 1973
Founding and Former Series Editors:
Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen
Editorial Board
David Hutchison
Lancaster University, Lancaster, UK
Takeo Kanade
Carnegie Mellon University, Pittsburgh, PA, USA
Josef Kittler
University of Surrey, Guildford, UK
Jon M. Kleinberg
Cornell University, Ithaca, NY, USA
Friedemann Mattern
ETH Zurich, Zurich, Switzerland
John C. Mitchell
Stanford University, Stanford, CA, USA
Moni Naor
Weizmann Institute of Science, Rehovot, Israel
C. Pandu Rangan
Indian Institute of Technology Madras, Chennai, India
Bernhard Steffen
TU Dortmund University, Dortmund, Germany
Demetri Terzopoulos
University of California, Los Angeles, CA, USA
Doug Tygar
University of California, Berkeley, CA, USA
More information about this series at http://www.springer.com/series/7407
á ó
Ivan Dimov Istv n Farag
(cid:129)
Lubin Vulkov (Eds.)
Finite Difference Methods
Theory and Applications
7th International Conference, FDM 2018
–
Lozenetz, Bulgaria, June 11 16, 2018
Revised Selected Papers
123
Editors
IvanDimov LubinVulkov
IICT University of Rousse
BulgarianAcademy of Sciences Rousse, Bulgaria
Sofia,Bulgaria
István Faragó
EötvösLorándUniversity
Budapest, Hungary
ISSN 0302-9743 ISSN 1611-3349 (electronic)
Lecture Notesin Computer Science
ISBN 978-3-030-11538-8 ISBN978-3-030-11539-5 (eBook)
https://doi.org/10.1007/978-3-030-11539-5
LibraryofCongressControlNumber:2018967313
LNCSSublibrary:SL1–TheoreticalComputerScienceandGeneralIssues
©SpringerNatureSwitzerlandAG2019
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartofthe
material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,
broadcasting, reproduction on microfilms or in any other physical way, and transmission or information
storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynow
knownorhereafterdeveloped.
Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthispublication
doesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevant
protectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbookare
believedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsortheeditors
give a warranty, express or implied, with respect to the material contained herein or for any errors or
omissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictionalclaimsin
publishedmapsandinstitutionalaffiliations.
ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Preface
The papers published in this volume were presented at FDM: T&A 2018, the 7th
International Conference on Finite Difference Methods: Theory and Applications,
which was held in Lozenetz, Bulgaria, June 11–16, 2018. The conference was orga-
nized by the Division of Numerical Analysis and Statistics (DNAS), University of
Rousse, in cooperation with the Department of Parallel Algorithms, Institute of
InformationandCommunicationTechnologies,BAS,Sofia.Thisconferencecontinued
the tradition of four previous meetings: 1997 in Rousse (Bulgaria) organized by the
Division of Numerical Analysis and Statistics; 1998 in Minsk (Belarus), organized by
the Institute of Mathematics, Belarus Academy of Science; 2000 in Palanga,
(Lithuania), organized by the Institute of Mathematics and Informatics (Vilnus); and
2006, 2010, and 2014 in Lozenetz, (Bulgaria) organized by DNAS.
Thepurposeofthefirstthreeconferences(heldinBulgaria, BelarusandLithuania)
wastobringtogetherscientistsfromtheEastandWesttoexchangeideasandestablish
researchcooperationforthenextfewyears.Contactamongscientistshasbecomemore
regular and we can be proud of our contribution. The conference lectures were pre-
sented by the university researchers and practical industry engineers, including
researchersworkinginappliedmathematics,numericalanalysis,andcomputerscience.
The key lectures reviewed recent results of theory and different applications offinite
difference methods.
The general theme for FDM: T&A 2018 was finite difference and combined finite
difference, finite element methods and various applications in physics, chemistry,
engineering, biology, and finance. Many modern and new numerical techniques were
discussedandpresentedattheconferencesuchassplittingtechniques,Green’sfunction
method, multigrid methods, immersed interface method, etc.
Nine Special Sessions were organized by leading specialists of the field.
1. Novel Methods in Computational Finance (by M. Ehrhardt, C. Mishra, and
S. Wang)
2. AdvancedNumericalandAppliedStudiesofInverseProblems(byS.I.Kabanikhin
and M. A. Shishlenin)
3. Numerical Methods for Fractional-Derivative Problems and Applications (by
A. Alikhanov, R. Lazarov, and M. Stynes)
4. MeshfreeGeneralizedFiniteDifferenceMethods:FromTheorytoApplications(by
I. Michel, J. Kuhnert, and P. Suchde)
5. Reliable Difference Methods for Singularly Perturbed Problems (by G. Shishkin
and L. Shishkina)
6. IterativeSchemesforSolvingNonlinearModels(M.P.Vassileva,A.Cordero,and
J. R. Torregrosa)
7. Finite Differences Methods in Life Sciences (by G. Pena and J. A. Ferreira)
VI Preface
8. Asymptotic Analysis of Numerical Methods for Problems with Sharp Transition
Layers (by N. Nefedov)
9. Numerical Methods for Propagation Processes (by P. Csomos and I. Farago)
Wethanktoourcolleaguesfortheirhelpintheorganizationofthisconference.We
especiallythank M. Koleva for preparationofthis volume.We arealso grateful tothe
organizers of the Minisymposia.
The8thInternationalConferenceFDM:T&A2022willbeorganizedinJune2022.
October 2018 Ivan Dimov
István Faragó
Lubin Vulkov
Organization
FDM:T&A2018wasorganizedbytheDivisionofNumericalAnalysisandStatistics,
University of Ruse Angel Kanchev, Bulgaria, in cooperation with the Department of
Parallel Algorithms, Institute of Information and Communication Technologies,
Bulgarian Academy of Sciences, Sofia.
TheconferencewaspartlysupportedbytheBulgarianNationalScienceFundunder
Project DN 12/4 from 2017, “Advanced analytical and numerical methods for
nonlinear differential equations with applications in finance and environmental
pollution.”
Scientific Committee
Anatoly Alikhanov Russian Academy of Sciences, Russia
Claudio Cuevas Universidade Federal Permabuco, Brazil
Ivan Dimov Bulgarian Academy of Sciences, Bulgaria
Matthias Ehrhardt Bergische Universität Wuppertal, Germany
István Faragó Eötvös Loránd University, Hungary
Martin Gander Université de Genève, Switzerland
Raytcho Lazarov Texas A&M University, USA
Piotr Matus Institute of Mathematics, NAS, Belarus
Nikolay Nefedof Lomonosov Moscow State University, Russia
Vladimir Shaydurov Russian Academy of Sciences, Russia
Grigorii Shishkin Russian Academy of Sciences, Russia
Martin Stynes BeijingComputationalScienceResearchCenter,China
Petr Vabishchevich Russian Academy of Sciences, Russia
Song Wang Curtin University, Australia
Ludmil Zikatanov Pennsylvania State University, USA
Local Organizers
Luben Vulkov Ruse University Angel Kanchev, Bulgaria
(Chairperson)
Ivanka Angelova Ruse University Angel Kanchev, Bulgaria
Tatiana Chernogorova Sofia University St. Kliment Ohridski, Bulgaria
Slavi Georgiev Ruse University Angel Kanchev, Bulgaria
Miglena Koleva Ruse University Angel Kanchev, Bulgaria
Contents
Invited Papers
From a Geometrical Interpretation of Bramble-Hilbert Lemma
to a Probability Distribution for Finite Element Accuracy. . . . . . . . . . . . . . . 3
Joel Chaskalovic and Franck Assous
A High Order Method on Graded Meshes for a Time-Fractional
Diffusion Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Hu Chen and Martin Stynes
Numerical Solving a Boundary Value Problem for the Eikonal Equation . . . . 28
Alexander G. Churbanov and Petr N. Vabishchevich
Iterative Semi-implicit Splitting Methods for Stochastic Chemical Kinetics. . . 35
Jürgen Geiser
The Application of a Special Hermite Finite Element Coupled
with Collocation to the Diffusion Equation. . . . . . . . . . . . . . . . . . . . . . . . . 48
Lidiya Gileva, Evgeniya Karepova, and Vladimir Shaydurov
A 2nd-Order Numerical Scheme for Fractional Ordinary
Differential Equation Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
W. Li and S. Wang
Blow-Up of Fronts in Burgers Equation with Nonlinear Amplification:
Asymptotics and Numerical Diagnostics. . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Dmitry Lukyanenko and Nikolay Nefedov
Improved Computer Scheme for a Singularly Perturbed Parabolic
Convection–Diffusion Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Grigorii Shishkin and Lidia Shishkina
On Ignorance Regions and Spatial Aspects for South American sea lion
(Otaria byronia) Operational Interaction with the Artisan Gillnet
Fishery in Chile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Milan Stehlík, Jean Paul Maidana, Claudia Navarro Villarroel,
Maritza Sepúlveda, and Doris Oliva
Finite Difference Scheme for Stochastic Differential Games with Several
Singular Control Variables and Its Environmental Application . . . . . . . . . . . 102
Hidekazu Yoshioka and Yuta Yaegashi
X Contents
Stability Properties of Repeated Richardson Extrapolation Applied
Together with Some Implicit Runge-Kutta Methods. . . . . . . . . . . . . . . . . . . 114
Zahari Zlatev, Ivan Dimov, István Faragó, Krassimir Georgiev,
and Ágnes Havasi
Contributed Papers
Computer Modeling of Control the Thermal Imaging System Surveillance. . . 129
Tatiana Akimenko and Ekaterina Filippova
Generalized Multiscale Finite Element Method for Elasticity Problem
in Fractured Media . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
V. Alekseev, A. Tyrylgin, and M. Vasilyeva
Automatic Time Step Selection for Numerical Solution
of Neutron Diffusion Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
A.V.Avvakumov,V.F.Strizhov,P.N.Vabishchevich,andA.O.Vasilev
Local Convergence Results for an Optimal Iterative Method
for Multiple Roots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Ramandeep Behl, Eulalia Martínez, Fabricio Cevallos,
and Ali Saleh Alshomrani
Spline Iterative Method for Pantograph Type Functional
Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Alexandru Mihai Bica, Mircea Curila, and Sorin Curila
On Gas Dynamic Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
S.V.Bogomolov,N.B.Esikova,A.E.Kuvshinnikov,andP.N.Smirnov
The Error Analysis of Finite Difference Approximation for a System
of Singularly Perturbed Semilinear Reaction-Diffusion Equations
with Discontinuous Source Term. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
S. Chandra Sekhara Rao and Sheetal Chawla
Efficiency and Stability of a Family of Iterative Schemes
for Solving Nonlinear Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Alicia Cordero, Ivan Giménez, and Juan R. Torregrosa
Stability of a Family of Iterative Methods of Fourth-Order. . . . . . . . . . . . . . 193
Alicia Cordero, Lucía Guasp, and Juan R. Torregrosa
Multidimensional Real Dynamics for High-Order Processes . . . . . . . . . . . . . 201
Alicia Cordero, Javier G. Maimó, Juan R. Torregrosa,
and Maria P. Vassileva
