Stochastic Numerics for Mathematical Physics


Book Description

This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.




Supersonic Flow and Shock Waves


Book Description

Courant and Friedrich's classical treatise was first published in 1948 and tThe basic research for it took place during World War II. However, many aspects make the book just as interesting as a text and a reference today. It treats the dynamics of compressible fluids in mathematical form, and attempts to present a systematic theory of nonlinear wave propagation, particularly in relation to gas dynamics. Written in the form of an advanced textbook, it should appeal to engineers, physicists and mathematicians alike.







Grid Generation Methods


Book Description

This text is an introduction to methods of grid generation technology in scientific computing. Special attention is given to methods developed by the author for the treatment of singularly-perturbed equations, e.g. in modeling high Reynolds number flows. Functionals of conformality, orthogonality, energy and alignment are discussed.




Trends in the Analysis and Design of Marine Structures


Book Description

Trends in the Analysis and Design of Marine Structures is a collection of the papers presented at MARSTRUCT 2019, the 7th International Conference on Marine Structures held in Dubrovnik, Croatia, 6-8 May 2019. The MARSTRUCT series of Conferences started in Glasgow, UK in 2007, the second event of the series having taken place in Lisbon, Portugal in March 2009, the third in Hamburg, Germany in March 2011, the fourth in Espoo, Finland in March 2013, the fifth in Southampton, UK in March 2015, and the sixth in Lisbon, Portugal in May 2017. This Conference series specialises in dealing with Ships and Offshore Structures, addressing topics in the fields of: - Methods and Tools for Loads and Load Effects - Methods and Tools for Strength Assessment - Experimental Analysis of Structures - Materials and Fabrication of Structures - Methods and Tools for Structural Design and Optimisation - Structural Reliability, Safety and Environmental Protection. Trends in the Analysis and Design of Marine Structures is an essential document for academics, engineers and all professionals involved in the area of analysis and design of Ships and Offshore Structures. About the series: The ‘Proceedings in Marine Technology and Ocean Engineering’ series is devoted to the publication of proceedings of peer-reviewed international conferences dealing with various aspects of ‘Marine Technology and Ocean Engineering’. The Series includes the proceedings of the following conferences: the International Maritime Association of the Mediterranean (IMAM) conferences, the Marine Structures (MARSTRUCT) conferences, the Renewable Energies Offshore (RENEW) conferences and the Maritime Technology (MARTECH) conferences. The ‘Marine Technology and Ocean Engineering’ series is also open to new conferences that cover topics on the sustainable exploration and exploitation of marine resources in various fields, such as maritime transport and ports, usage of the ocean including coastal areas, nautical activities, the exploration and exploitation of mineral resources, the protection of the marine environment and its resources, and risk analysis, safety and reliability. The aim of the series is to stimulate advanced education and training through the wide dissemination of the results of scientific research.




Optimal Methods for Ill-Posed Problems


Book Description

The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods described in the current book are used to solve a number of inverse problems in mathematical physics. Contents Modulus of continuity of the inverse operator and methods for solving ill-posed problems Lavrent’ev methods for constructing approximate solutions of linear operator equations of the first kind Tikhonov regularization method Projection-regularization method Inverse heat exchange problems




Operations Research in Transportation Systems


Book Description

The scientific monograph of a survey kind presented to the reader's attention deals with fundamental ideas and basic schemes of optimization methods that can be effectively used for solving strategic planning and operations manage ment problems related, in particular, to transportation. This monograph is an English translation of a considerable part of the author's book with a similar title that was published in Russian in 1992. The material of the monograph embraces methods of linear and nonlinear programming; nonsmooth and nonconvex optimization; integer programming, solving problems on graphs, and solving problems with mixed variables; rout ing, scheduling, solving network flow problems, and solving the transportation problem; stochastic programming, multicriteria optimization, game theory, and optimization on fuzzy sets and under fuzzy goals; optimal control of systems described by ordinary differential equations, partial differential equations, gen eralized differential equations (differential inclusions), and functional equations with a variable that can assume only discrete values; and some other methods that are based on or adjoin to the listed ones.




Finite-Dimensional Variational Inequalities and Complementarity Problems


Book Description

This is part two of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It details algorithms for solving finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.




Stochastic Computing: Techniques and Applications


Book Description

This book covers the history and recent developments of stochastic computing. Stochastic computing (SC) was first introduced in the 1960s for logic circuit design, but its origin can be traced back to von Neumann's work on probabilistic logic. In SC, real numbers are encoded by random binary bit streams, and information is carried on the statistics of the binary streams. SC offers advantages such as hardware simplicity and fault tolerance. Its promise in data processing has been shown in applications including neural computation, decoding of error-correcting codes, image processing, spectral transforms and reliability analysis. There are three main parts to this book. The first part, comprising Chapters 1 and 2, provides a history of the technical developments in stochastic computing and a tutorial overview of the field for both novice and seasoned stochastic computing researchers. In the second part, comprising Chapters 3 to 8, we review both well-established and emerging design approaches for stochastic computing systems, with a focus on accuracy, correlation, sequence generation, and synthesis. The last part, comprising Chapters 9 and 10, provides insights into applications in machine learning and error-control coding.