Christian Constanda Paul Harris Editors Integral Methods in Science and Engineering Analytic Treatment and Numerical Approximations Christian Constanda • Paul Harris Editors Integral Methods in Science and Engineering Analytic Treatment and Numerical Approximations Editors ChristianConstanda PaulHarris DepartmentofMathematics Computing,Engineering,andMathematics TheUniversityofTulsa UniversityofBrighton Tulsa,OK,USA Brighton,UK ISBN978-3-030-16076-0 ISBN978-3-030-16077-7 (eBook) https://doi.org/10.1007/978-3-030-16077-7 MathematicsSubjectClassification:45Exx,45E10,65R20,45D05 ©SpringerNatureSwitzerlandAG2019 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof thematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation, broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionorinformation storageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodology nowknownorhereafterdeveloped. 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Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface The international conferences on Integral Methods in Science and Engineering (IMSE) started in 1985 at the University of Texas–Arlington and, from 1996, continued biennially in a variety of venues around the world. These events bring together specialists who make use of integration techniques as essential tools in theirresearch.Thesetypesofproceduresarecharacterizedbygenerality,elegance, and efficiency, which are essential ingredients in the work of a wide category of practitioners. Thetimeandplaceofthefirst14IMSEconferencesarelistedbelow: 1985,1990: UniversityofTexas–Arlington,USA 1993: TohokuUniversity,Sendai,Japan 1996: UniversityofOulu,Finland 1998: MichiganTechnologicalUniversity,Houghton,MI,USA 2000: Banff,AB,Canada(organizedbytheUniversityofAlberta,Edmon- ton) 2002: UniversityofSaint–Étienne,France 2004: UniversityofCentralFlorida,Orlando,FL,USA 2006: NiagaraFalls,ON,Canada(organizedbytheUniversityofWaterloo) 2008: UniversityofCantabria,Santander,Spain 2010: UniversityofBrighton,UK 2012: BentoGonçalves,Brazil(organizedbytheFederalUniversityofRio GrandedoSul) 2014: KarlsruheInstituteofTechnology,Germany 2016: UniversityofPadova,Italy The2018event,the15thintheseries,washostedbytheUniversityofBrighton, UK, July 16–20, gathering participants from 16 countries on 5 continents, whose high-quality presentations consolidated the well-deserved reputation of the IMSE conferences as a vehicle for scientists and engineers to communicate their most recentresultsandideasandtoforgecontactsforfutureprofessionalcollaboration. v vi Preface The Organizing Committee of the conference, assisted by Laura Williams and RichardHuckofSouthwestConferences,wascomprisedof: PaulHarris(UniversityofBrighton),Chairman JennyVenton(UniversityofBrighton) DmitrySavostyanov(UniversityofBrighton) The accomplishments of the IMSE 2018 meeting were due to a large extent to the financial support received from the School of Computing, Engineering and Mathematics at the University of Brighton. The participants and the Organizing Committeewishtothankthisacademicbodyforitsunderwritingofthesuccessof theconference. IMSE2018includedtwominisymposia: AsymptoticAnalysis:HomogenizationandThinStructures;organizer:M.E.Pérez– Martínez(UniversityofCantabria) Boundary:DomainIntegralEquations;organizer:S.Mikhailov(BrunelUniversity London) The next IMSE conference will be held at the University of St. Petersburg, Russia, July 13–17, 2020. Further details will be posted in due course on the conferencewebsite. The peer-reviewed chapters of this volume, arranged alphabetically by first author’s name, consist of 36 papers presented in Brighton. The editors would like tothankthereviewersfortheirvaluablehelpandthestaffatBirkhäuser–NewYork fortheircourteousandprofessionalhandlingofthepublicationprocess. Tulsa,OK,USA ChristianConstanda Brighton,UK PaulHarris January2019 The International Steering Committee of IMSE ChristianConstanda(TheUniversityofTulsa),Chairman BardoE.J.Bodmann(FederalUniversityofRioGrandedoSul) HaroldoF.deCamposVelho(INPE,SaõJosédosCampos) PaulJ.Harris(UniversityofBrighton) AndreasKirsch(KarlsruheInstituteofTechnology) MirelaKohr(Babes–BolyaiUniversityofCluj–Napoca) MassimoLanzadeCristoforis(UniversityofPadova) SergeyMikhailov(BrunelUniversityLondon) DorinaMitrea(UniversityofMissouri–Columbia) MariusMitrea(UniversityofMissouri–Columbia) DavidNatroshvili(GeorgianTechnicalUniversity) MariaPerel(St.PetersburgStateUniversity) MariaEugeniaPérez–Martínez(UniversityofCantabria) OvadiaShoham(TheUniversityofTulsa) IainW.Stewart(UniversityofDundee) Continuing a tradition started at the preceding conference, IMSE 2018 hosted an exhibition of digital art that consisted of five portraits of participants and a special conference poster, executed by artist Walid Ben Medjedel using different techniques.Theexhibitsweremuchappreciatedbytheparticipants,who,asbefore, commentedontherelationshipbetweendigitalartandmathematics. The portraits and the poster have been reduced to scale and reproduced on the nextpage. vii viii TheInternationalSteeringCommitteeofIMSE DigitalArtbyWalidBenMedjedel ChristianConstanda:comics JennyVenton:watercolor PaulHarris:caricature PaulHarris:portrait MariusMitrea:retrovintage IMSE2018specialposter Contents 1 Singularity Subtraction for Nonlinear Weakly Singular IntegralEquationsoftheSecondKind .................................. 1 MarioAhues,FilomenaD.d’Almeida,RosárioFernandes, andPauloB.Vasconcelos 2 OntheFlowofaViscoplasticFluidinaThinPeriodicDomain....... 15 MaríaAnguianoandRenataBunoiu 3 q-CalculusFormalismforNon-extensiveParticleFilter ............... 25 Amarisio S. Araújo, Helaine C. M. Furtado, andHaroldoF.deCamposVelho 4 Two-Operator Boundary-Domain Integral Equations forVariable-CoefficientDirichletProblemwithGeneralData........ 37 TsegayeG.Ayele 5 Two-Operator Boundary-Domain Integral Equations forVariableCoefficientDirichletProblemin2D ....................... 53 TsegayeG.AyeleandSolomonT.Bekele 6 SolutionofaHomogeneousVersionofLoveTypeIntegral EquationinDifferentAsymptoticRegimes.............................. 67 LaurentBaratchart,JulietteLeblond,andDmitryPonomarev 7 ASemi-analyticalSolutionforOne-DimensionalOil DisplacementbyMiscibleGasinaHomogeneousPorous Medium...................................................................... 81 LuanaC.M.Cantagesso,LuaraK.S.Sousa,TamiresA.Marotto, AnnaM.Radovanovic,AdolfoPuimePires,andAlvaroM.M.Peres 8 BendingofElasticPlates:GeneralizedFourierSeriesMethod fortheRobinProblem ..................................................... 97 ChristianConstandaandDaleDoty ix x Contents 9 TheAdjointSpectralGreen’sFunctionMethodAppliedto DirectandInverseNeutralParticleSource–DetectorProblems ...... 111 JesúsP.Curbelo,OdairP.daSilva,andRicardoC.Barros 10 RelaxationofPeriodicandNonstandardGrowthIntegrals byMeansofTwo-ScaleConvergence..................................... 123 JoelFotsoTachago,HubertNnang,andElviraZappale 11 AStiffProblem:StationaryWavesandApproximations.............. 133 DelfinaGómez,SantiagoNavazo-Esteban, andMaría-EugeniaPérez-Martínez 12 ModellingCreepinConcreteUnderaVariableExternalLoad....... 149 LayalHakim 13 ACombinedBoundaryElementandFiniteElementModel ofCellMotionduetoChemotaxis ........................................ 163 PaulJ.Harris 14 NumericalCalculationbyQuadruplePrecisionHigherOrder TaylorSeriesMethodofthePythagoreanProblem ofThreeBodies ............................................................. 173 HiroshiHirayama 15 ShapeOptimizationforInteriorNeumannandTransmission Eigenvalues.................................................................. 185 AndreasKleefeld 16 OntheIntegro-DifferentialRadiativeConductiveTransfer Equation:AModifiedDecompositionMethod.......................... 197 CibeleA.Ladeia,BardoE.J.Bodmann,andMarcoT.Vilhena 17 PeriodicTransmissionProblemsfortheHeatEquation ............... 211 PaoloLuzziniandPaoloMusolino 18 OnUnitedBoundary-DomainIntegro-DifferentialEquations for Variable Coefficient Dirichlet Problem with General Right-HandSide............................................................ 225 SergeyE.MikhailovandZenebeW.Woldemicheal 19 RescalingandTraceOperatorsinFractionalSobolevSpaces onBoundedLipschitzDomainswithPeriodicStructure............... 237 SergeyE.Mikhailov,PaoloMusolino,andJuliaOrlik 20 DesignandPerformanceofaMultiphaseFlowManifold.............. 253 MobinaMohammadikharkeshi,AsadMolayari,RaminDabirian, RamS.Mohan,andOvadiaShoham