Product Description: Edited by the pioneer and foremost authority on the subject, here is the first book to assemble in one resource the latest techniques and results of the leading theoreticians and practitioners of FD-TD computational electromagnetics modelling...read more (view table of contents, read Amazon.com's description)

Product Description: This book is devoted to new classes of parabolic differential and pseudo-differential equations extensively studied in the last decades, such as parabolic systems of a quasi-homogeneous structure, degenerate equations of the Kolmogorov type, pseudo-differential parabolic equations, and fractional diffusion equations...read more

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Product Description: From the Preface: "The object of this book is to provide a simple and connected account of the subject of Finite Differences and to present the theory in a form which can be readily applied ...not only the useful material of Boole ...read more

Product Description: This book, which is published in two volumes, studies heat transfer problems by modern numerical methods. Basic mathematical models of heat transfer are considered. The main approaches to the analysis of the models by traditional means of applied mathematics are described...read more (view table of contents, read Amazon.com's description)

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Using an engineering perspective, it reviews and compares numerical methods and more recent contributions for solving both moving boundary and boundary value problems. Describes current advances in the finite difference solution of linear and nonlinear partial differential equations. Algorithmic manipulations which enhance the computational efficiency are incorporated into the overall schemes.

Product Description: This new book deals with the construction of finite-difference (FD) algorithms for three main types of equations: elliptic equations, heat equations, and gas dynamic equations in Lagrangian form. These methods can be applied to domains of arbitrary shapes...read more (view table of contents, read Amazon.com's description)

Product Description: Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non­ stationary problems of mathematical physics...read more

Product Description: Bridges the gap between FDTD theory and the implementation of practical simulation techniques This is the first publication that guides readers step by step through the implementation of electromagnetic simulation techniques based on FDTD methods...read more

Product Description: A straightforward, easy-to-read introduction to the finite-difference time-domain (FDTD) method Finite-difference time-domain (FDTD) is one of the primary computational electrodynamics modeling techniques available. Since it is a time-domain method, FDTD solutions can cover a wide frequency range with a single simulation run and treat nonlinear material properties in a natural way...read more

Product Description: An interrelated account of many of the most important finite difference methods and their results, this text is geared toward upper-level undergraduates and graduate students. Topics include hyperbolic equations in two independent variables, parabolic and elliptic equations, and initial-value problems in more than two independent variables...read more

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.

Product Description: Finite Difference Methods in Heat Transfer presents a clear, step-by-step delineation of finite difference methods for solving engineering problems governed by ordinary and partial differential equations, with emphasis on heat transfer applications...read more (view table of contents, read Amazon.com's description)

Product Description: Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion...read more

Product Description: This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. Originally published in 1989, its objective remains to clearly present the basic methods necessary to perform finite difference schemes and to understand the theory underlying these schemes...read more

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Product Description: Most texts on computational methods are borne out of research activities at postgraduate study programs, and this is no exception. After being introduced to the boundary element method (BEM) (then referred to as the boundary integral equation method (BIEM)) in 1981 by Prof...read more

Product Description: This book covers high order finite difference methods for time dependent PDE. It gives an overview of the basic theory and construction principles by using model examples. The book also contains a general presentation of the techniques and results for well-posedness and stability, with inclusion of the three fundamental methods of analysis both for PDE in its original and discretized form: the Fourier transform, the eneregy method and the Laplace transform...read more

Tells how the largest aircraft that was ever flown was destroyed, and describes the investigation that followed.