Books in the Numerical Mathematics and Scientific Computation series

Written by leading experts in the field, two of whom have actively contributed to Fortran 2018, Modern Fortran Explained is a complete and authoritative description of Fortran in its latest form

A practical graduate text on Scientific Computing with a focus on numerical solution of partial differential equations and numerical linear algebra. This book, and its associated freely downloadable MATLAB software, is relevant to engineers, applied mathematicians, numerical analysts, and people working in interdisciplinary Scientific Computing.

A clear and thorough description of the latest versions of Fortran by leading experts in the field. It is intended for new and existing users of the language, and for all those involved in scientific and numerical computing. It is suitable as a textbook for teaching and as a handy reference for practitioners.

Describes the principles and history behind the use of Krylov subspace methods in science and engineering. The outcome of the analysis is very practical and indicates what can and cannot be expected from the use of Krylov subspace methods, challenging some common assumptions and justifications of standard approaches.

This text, based on the author's teaching at Ecole Polytechnique, introduces the reader to the world of mathematical modelling and numerical simulation. Including numerous exercises and examples, this is an ideal text for advanced students in Applied Mathematics, Engineering, Physical Science and Computer Science.

This unique book describes, analyses, and improves various approaches and techniques for the numerical solution of delay differential equations. It includes a list of available codes and also aids the reader in writing his or her own.

Provides a survey of the "Lattice Boltzmann equation" (LBE) theory and its major applications. Suitable for scientists dealing with complex system dynamics, this book also portrays future developments in allied areas of science, such as material science, biology and others, where fluid motion plays a distinguished role.

Providing an introduction to the theoretical, practical, and numerical aspects of image registration, with emphasis on medical imaging, this illustrated text describes various techniques. It discusses the basic mathematical principles, including aspects from approximation theory, numerics, partial differential equations, and statistics.

A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods.

Inverse eigenvalue problems arise in a remarkable variety of applications, and associated with any inverse eigenvalue problem are two fundamental questions - the theoretical issue of solvability and the practical issue of computability. This text discusses the fundamental questions, many applications, and mathematical properties.

Intersecting two large research areas - numerical analysis and applied probability/queuing theory - this book is an introduction to the numerical solution of structured Markov chains, which have a wide applicability in queueing theory and stochastic modelling. It provides a systematic treatment of the important families of these chains.

This new edition of Applied Shape Optimization for Fluids deals with shape optimization problems for fluids, with the equations needed for their understanding (Euler and Navier Strokes, but also those for microfluids) and with the numerical simulation of these problems.

Nonlinear elliptic problems are important to Mathematics, Science and Engineering. This is the first and only book to handle systematically the different numerical methods for these problems. Several long open problems are solved here for the first time.

The subject of sparse matrices has its root in such diverse fields as management science, power systems analysis, surveying, circuit theory, and structural analysis. Efficient use of sparsity is a key to solving large problems in many fields. This book provides both insight and answers for those attempting to solve these problems.

A text based on the author's course that introduces graduates to the basics of wavelet methods for partial differential equations and describes the construction and analysis of adaptive wavelet methods.

This volume presents the mathematical theory of the finite element method and focuses on the question of how reliable computed results really are. Many computational examples illustrate the importance of the theoretical conclusions for practical computations.

Domain decomposition methods are well suited to design algorithms for parallel computers. These allow researchers to tackle large-scale mathematical problems in aerodynamics and other areas of science and engineering. This book discusses the principles of the method in connection with a wide variety of both theoretical and practical problems.

This clear and comprehensive text focuses on mathematical and numerical techniques for the simulation of magnetohydrodynamic phenomena, with an emphasis on industrial applications. Aimed at research mathematicians, engineers and physicists, as well as those working in industry, the approach is highly mathematical and based on solid numerical analysis.

Deals with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed.

This reference provides an up to date and sound theoretical foundation for finite element methods in computational electromagnetism. The emphasis is on finite element methods for scattering problems that involve the solution of Maxwell's equations on infinite domains, and special attention is given to error analysis of edge FEM that are particularly well suited to Maxwell's equations .

Numerical and computational methods play a major role in modelling compressible flow and are important tools in solving fluid dynamical problems faced in many areas of science and technology. This book thoroughly surveys and analyzes up-to-date methods, while reviewing the basic theoretical mathematical analysis.

This book describes algorithms and mathematical fundamentals of the widely used FITBACK package for curve and surface fitting with splines. Features included are automatic knot selection, error smoothing and data reduction. The practical side of this software is illustrated with many examples taken from different disciplines in engineeering and medicine.

Sphere-oriented mathematics is the focus of this text, which presents new structures and methods by which sophisticated measurements and observations can be handled efficiently, thus reducing time and costs.

Covers the significant progress in multi-domain spectral methods at both the fundamental and application level. This book includes material on discontinuous Galerkin methods, non-tensorial nodal spectral element methods in simplex domains, and stabilisation and filtering techniques.

This title is an introduction to the mathematical analysis of p- and hp-finite elements applied to elliptic problems in solid and fluid mechanics, and is suitable for graduate students and researchers who have had some prior exposure to finite element methods (FEM).

This text provides an introduction to the methods of parallel optimization by introducing parallel computing ideas and techniques into both optimization theory and numerical algorithms for large-scale optimization problems.

Orthogonal polynomials are a widely used class of mathematical functions that are helpful in the solution of many important technical problems. This book provides, for the first time, a systematic development of computational techniques, including a suite of computer programs in Matlab downloadable from the Internet, to generate orthogonal polynomials of a great variety.

A new paperback edition of Wilkinson's classic, pioneering text on the computation of matrix eigenvalues. One of the most important and widely-read books on numerical analysis ever published.

Brings together much work that has appeared from 1984 to 1994 in the general area of adaptive numerical solution of partial differential equations insofar as it bears on and has been stimulated by the MFE idea.

This is an up-to-date exposition of the current method of using numerical methods to solve ordinary differential equations in a parallel computing environment. Consideration is given to boundary value problems and partial differential equations.