Time-Dependent Problems and Difference Methods

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.

This book contains contributions from interdisciplinary scientists to collectively address the issue of targeting carbohydrate recognition for the development of novel therapeutic and diagnostic agents. The book covers (1) biological problems involving carbohydrate recognition, (2) structural factors mediating carbohydrate recognition, (3) design and synthesis of lectin mimics that recognize carbohydrate ligands with high specificity and affinity, and (4) modulation of biological and pathological processes through carbohydrate recognition.

This book studies methods to concretely address inverse problems. An inverse problem arises when the causes that produced a given effect must be determined or when one seeks to indirectly estimate the parameters of a physical system. The author uses practical examples to illustrate inverse problems in physical sciences. He presents the techniques and specific methods chosen to solve inverse problems in a general domain of application, choosing to focus on a small number of methods that can be used in most applications. This book is aimed at readers with a mathematical and scientific computing background. Despite this, it is a book with a practical perspective. The methods described are applicable, have been applied, and are often illustrated by numerical examples.

The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.

The focus of this book is on «ill-posed inverse problems». These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built. For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has since recognized that these matters are more interesting and they have become the subject of much greater enthusiasm. From the application field’s point of view, a significant part of the book is devoted to conventional subjects in the field of inversion: biological and medical imaging, astronomy, non-destructive evaluation, processing of video sequences, target tracking, sensor networks and digital communications. The variety of chapters is also clear, when we examine the acquisition modalities at stake: conventional modalities, such as tomography and NMR, visible or infrared optical imaging, or more recent modalities such as atomic force imaging and polarized light imaging.

Sensory evaluation is a scientific discipline used to evoke, measure, analyse and interpret responses to products perceived through the senses of sight, smell, touch, taste and hearing. It is used to reveal insights into the way in which sensory properties drive consumer acceptance and behaviour, and to design products that best deliver what the consumer wants. It is also used at a more fundamental level to provide a wider understanding of the mechanisms involved in sensory perception and consumer behaviour. Sensory perception of products alters considerably during the course of consumption/use. Special techniques are used in product development to measure these changes in order to optimise product delivery to consumers. Time-Dependent Measures of Perception in Sensory Evaluation explores the many facets of time-dependent perception including mastication and food breakdown, sensory-specific satiety and sensory memory. Both traditional and cutting-edge techniques and applications used to measure temporal changes in sensory perception over time are reviewed, and insights into the way in which sensory properties drive consumer acceptance and behaviour are provided. This book will be a valuable resource for sensory professionals working in academia and industry, including sensory scientists, practitioners, trainers and students; and industry-based researchers in QA/QC, R&D and marketing.

Interdisciplinarity research results from a growing need for multi-perspective methods, and knowledge on complex and multifaceted objects of study. It is not simply scientific research that involves several disciplines, but ultimately, the aim is confronting this knowledge and – if possible – articulating it coherently. Using specific examples, Methods and Interdisciplinarity categorizes the different modes of interdisciplinarity and discusses the mechanisms of hybridization between them. On the one hand, the book shows how the same issue can be treated according to various points of view from several disciplines, which can give rise to complementary or even contradictory knowledge. On the other hand, it illustrates how methods from some disciplines make it possible to articulate the qualitative or quantitative approaches of others.

Written and edited by a group of renowned specialists in the field, this outstanding new volume addresses primary computational techniques for developing new technologies in soft computing. It also highlights the security, privacy, artificial intelligence, and practical approaches needed by engineers and scientists in all fields of science and technology. It highlights the current research, which is intended to advance not only mathematics but all areas of science, research, and development, and where these disciplines intersect. As the book is focused on emerging concepts in machine learning and artificial intelligence algorithmic approaches and soft computing techniques, it is an invaluable tool for researchers, academicians, data scientists, and technology developers. The newest and most comprehensive volume in the area of mathematical methods for use in real-time engineering, this groundbreaking new work is a must-have for any engineer or scientist’s library. Also useful as a textbook for the student, it is a valuable contribution to the advancement of the science, both a working handbook for the new hire or student, and a reference for the veteran engineer.

The ultimate guide to trading systems, fully revised and updated For nearly thirty years, professional and individual traders have turned to Trading Systems and Methods for detailed information on indicators, programs, algorithms, and systems, and now this fully revised Fifth Edition updates coverage for today's markets. The definitive reference on trading systems, the book explains the tools and techniques of successful trading to help traders develop a program that meets their own unique needs. Presenting an analytical framework for comparing systematic methods and techniques, this new edition offers expanded coverage in nearly all areas, including trends, momentum, arbitrage, integration of fundamental statistics, and risk management. Comprehensive and in-depth, the book describes each technique and how it can be used to a trader's advantage, and shows similarities and variations that may serve as valuable alternatives. The book also walks readers through basic mathematical and statistical concepts of trading system design and methodology, such as how much data to use, how to create an index, risk measurements, and more. Packed with examples, this thoroughly revised and updated Fifth Edition covers more systems, more methods, and more risk analysis techniques than ever before. The ultimate guide to trading system design and methods, newly revised Includes expanded coverage of trading techniques, arbitrage, statistical tools, and risk management models Written by acclaimed expert Perry J. Kaufman Features spreadsheets and TradeStation programs for a more extensive and interactive learning experience Provides readers with access to a companion website loaded with supplemental materials Written by a global leader in the trading field, Trading Systems and Methods, Fifth Edition is the essential reference to trading system design and methods updated for a post-crisis trading environment.

Offers timely and comprehensive coverage of dynamic system reliability theory This book focuses on hot issues of dynamic system reliability, systematically introducing the reliability modeling and analysis methods for systems with imperfect fault coverage, systems with function dependence, systems subject to deterministic or probabilistic common-cause failures, systems subject to deterministic or probabilistic competing failures, and dynamic standby sparing systems. It presents recent developments of such extensions involving reliability modelling theory, reliability evaluation methods, and features numerous case studies based on real-world examples. The presented dynamic reliability theory can enable a more accurate representation of actual complex system behavior, thus more effectively guiding the reliable design of real-world critical systems. Dynamic System Reliability: Modelling and Analysis of Dynamic and Dependent Behaviors begins by describing the evolution from the traditional static reliability theory to the dynamic system reliability theory, and provides a detailed investigation of dynamic and dependent behaviors in subsequent chapters. Although written for those with a background in basic probability theory and stochastic processes, the book includes a chapter reviewing the fundamentals that readers need to know in order to understand contents of other chapters which cover advanced topics in reliability theory and case studies. The first book systematically focusing on dynamic system reliability modelling and analysis theory Provides a comprehensive treatment on imperfect fault coverage (single-level/multi-level or modular), function dependence, common cause failures (deterministic and probabilistic), competing failures (deterministic and probabilistic), and dynamic standby sparing Includes abundant illustrative examples and case studies based on real-world systems Covers recent advances in combinatorial models and algorithms for dynamic system reliability analysis Offers a rich set of references, providing helpful resources for readers to pursue further research and study of the topics Dynamic System Reliability: Modelling and Analysis of Dynamic and Dependent Behaviors is an excellent book for undergraduate and graduate students, and engineers and researchers in reliability and related disciplines.