Numerical Computations: Theory and Algorithms. Third International Conference, NUMTA 2019, Crotone, Italy, June 15–21, 2019, Revised Selected Papers
This volume, edited by Yaroslav D. Sergeyev and Dmitri E. Kvasov, contains selectedpeer-reviewed papers from the Third Triennial International Conference and SummerSchool on Numerical Computations: Theory and Algorithms (NUMTA 2019) held inLe Castella–Isola Capo Rizzuto (Crotone), Italy, during June 15–21, 2019.The NUMTA 2019 conference has continued the previous successful editions ofNUMTA that took place in 2013 and 2016 in Italy in the beautiful Calabria region.NUMTA 2019 was organized by the University of Calabria, Department of Com-puter Engineering, Modeling, Electronics and Systems Science, Italy, in cooperationwith the Society for Industrial and Applied Mathematics (SIAM), USA. This editionhad the high patronage of the municipality of Crotone–the city of Pythagoras and hisfollowers, the Pythagoreans. In fact, Pythagoras established thefirst Pythagoreancommunity in this city in the 6th century B.C. It was a very special feeling for theparticipants of NUMTA 2019 to visit these holy, for any mathematician, places with aconference dedicated to numerical mathematics.The goal of the NUMTA series of conferences is to create a multidisciplinary roundtable for an open discussion on numerical modeling nature by using traditional andemerging computational paradigms. Participants of the NUMTA 2019 conferencediscussed multiple aspects of numerical computations and modeling starting fromfoundations and philosophy of mathematics and computer science to advancednumerical techniques. New technological challenges and fundamental ideas fromtheoretical computer science, machine learning, linguistic, logic, set theory, and phi-losophy met the requirements, as well as fresh, new applications from physics,chemistry, biology, and economy.Researchers from both theoretical and applied sciences were invited to use thisexcellent opportunity to exchange ideas with leading scientists from different researchfields. Papers discussing new computational paradigms, relations with foundations ofmathematics, and their impact on natural sciences were particularly solicited. Specialattention during the conference was dedicated to numerical optimization techniquesand a variety of issues related to the theory and practice of the usage of infinities andinfinitesimals in numerical computations. In particular, there were a substantial numberof talks dedicated to a new promising methodology allowing one to execute numericalcomputations withfinite, infinite, and infinitesimal numbers on a new type of acomputational device–the Infinity Computer patented in the EU, Russia, and the USA.This edition of the NUMTA conference was dedicated to the 80th birthday ofProfessor Roman Strongin. For the past 50 years Roman Strongin has been a leader andan innovator in Global Optimization, an importantfield of Numerical Analysis havingnumerous real-life applications. His book on Global Optimization, published in 1978,was one of thefirst in the world on this subject. Now it is a classic and has been used bymany as theirfirst introduction and continued inspiration for Global Optimization.Since that time, Roman has published numerous books and more than 400 papers inseveral scientificfields and has been rewarded with many national and internationalhonors including the President of the Russian Federation Prize. For decades Romanserved as Dean, First Vice-Rector, and Rector of the famous Lobachevsky StateUniversity of Nizhny Novgorod. Since 2008 he has been President of this university.He is also Chairman of the Council of Presidents of Russian Universities,Vice-President of the Union of the Rectors of Russian Universities, and Chairmanof the Public Chamber of the Nizhny Novgorod Region.We are proud to inform you that 200 researchers from the following 30 countriesparticipated at the NUMTA 2019 conference: Argentina, Bulgaria, Canada, China,Czech Republic, Estonia, Finland, France, Germany, Greece, India, Iran, Italy, Japan,Kazakhstan, Latvia, Lithuania, the Netherlands, Philippines, Portugal, Romania,Russia, Saudi Arabia, South Korea, Spain, Switzerland, Thailand, Ukraine, the UK,and the USA.The following plenary lecturers shared their achievements with the NUMTA 2019participants:•Louis D’Alotto, USA:“Infinite games onfinite graphs using Grossone”•Renato De Leone, Italy:“Recent advances on the use of Grossone in optimizationand regularization problems”•Kalyanmoy Deb, USA:“Karush-Kuhn-Tucker proximity measure for convergenceof real-parameter single and multi-criterion optimization”•Luca Formaggia, Italy:“Numerical modeling offlow in fractured porous media andfault reactivation”•Jan Hesthaven, Switzerland:“Precision algorithms”•Francesca Mazzia, Italy:“Numerical differentiation on the Infinity Computer andapplications for solving ODEs and approximating functions”•Michael Vrahatis, Greece:“Generalizations of the intermediate value theorem forapproximations offixed points and zeroes of continuous functions”•Anatoly Zhigljavsky, UK:“Uniformly distributed sequences and space-filling”Moreover, the following tutorials were presented during the conference:•Roberto Natalini, Italy:“Vector kinetic approximations tofluid-dynamicsequations”•Yaroslav Sergeyev, Italy and Russia:“Grossone-based Infinity Computing withnumerical infinities and infinitesimals”•Vassili Toropov, UK:“Design optimization techniques for industrial applications:Challenges and progress”These proceedings of NUMTA 2019 consist of two volumes: Part I and Part II. Thebook you have in your hands is the second part containing peer-reviewed paperschosen from the general stream, plenary lectures, and small special sessions ofNUMTA 2019. Papers carefully selected from big special streams and sessions heldduring the conference have been collected in the Part I of the NUMTA 2019proceedings.viPrefaceThis volume contains 19 long papers and 32 short papers that were accepted forpublication after a thorough peer review process (required up to three review rounds forsome manuscripts) by the members of the NUMTA 2019 Program Committee andindependent reviewers. This volume also contains the paper of the winner (LorenzoFiaschi, Pisa, Italy) of the Springer Young Researcher Prize for the best NUMTA 2019presentation made by a young scientist. The support of the Springer LNCS editorialstaff and the sponsorship of the Young Researcher Prize by Springer are greatlyappreciated.The editors express their gratitude to institutions that have offered their generoussupport to the international conference NUMTA 2019. This support was essential forthe success of this event:–University of Calabria (Italy)–Department of Computer Engineering, Modeling, Electronics and Systems Scienceof the University of Calabria (Italy)–Italian National Group for Scientific Computation of the National Institute forAdvanced Mathematics F. Severi (Italy)–Institute of High Performance Computing and Networking of the National ResearchCouncil (Italy)–International Association for Mathematics and Computers in Simulation–International Society of Global OptimizationThe editors thank all the participants for their dedication to the success of NUMTA2019 and are grateful to the reviewers for their valuable work. Many thanks go to MariaChiara Nasso from the University of Calabria, Italy, for her kind support in the tech-nical editing of this volume.The next Triennial International Conference and Summer School NUMTA“Numerical Computations: Theory and Algorithms”will take place in 2022 in Italy.The editors of this volume, who are chairs of the NUMTA Scientific and OrganizingCommittees, respectively, invite all the participants of NUMTA 2019, and readers ofthis book, to submit their high-quality results to the next edition of this wonderful event.
Yaroslav D. Sergeyev, Dmitri E. Kvasov
This work is dedicated to modelling economic dynamics with random time scale. We propose a solution in the form a continuous time model where interactions of agents are random exchanges of finite portions of products and money at random points in time. In this framework, the economic agent determines the volume, but not the moments of the transactions and their order. The paper presents a correct formal description of optimal consumption and borrowing as a stochastic optimal control problem, which we study using the optimality conditions in the Lagrange’s form. The solution appears to have a boundary layer near the end of planning horizon where the optimal control satisfies the specific functional equation. This equation was studied numerically using the functional Newton method adapted to a two-dimensional case.