Books in the Handbook of Numerical Analysis series

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering.About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimizationEach chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further readingThe authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

These volumes cover all the major aspects of numerical analysis. This particular volume discusses the solution of equations in Rn, Gaussian elimination, techniques of scientific computer, the analysis of multigrid methods, wavelet methods, and finite volume methods.

Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations.Provides detailed, cutting-edge background explanations of existing algorithms and their analysisIdeal for readers working on the theoretical aspects of algorithm development and its numerical analysisPresents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applicationsWritten by leading subject experts in each field who provide breadth and depth of content coverage

This volume aims to cover all the major aspects of numerical analysis, serving as a reference work on the subject reflecting the current trends in the field.

This series aims to cover the major aspects of numerical analysis. The volume covers the techniques of scientific computing, numerical methods for solids and solution of equations in R.

Presents a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. This book uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences.

Suitable for graduate students in mathematics, sciences and engineering and technology, this volume covers advanced computational methods used in the mathematical analysis of chemical events and reactions. It covers both the numerics and modelling aspects.

From geometric integration and its applications, and linear programming and condition numbers under the real number computational model, to chaos in finite difference schemes, these essays explore the foundational issues of computational mathematics.

Part of a series of volumes, this work aims to cover all the major aspects of numerical analysis. It covers the basic methods of analysis under headings including finite difference methods, finite element methods, techniques of scientific computing, and numerical methods for fluids.

Provides an overview and insight in the way numerical methods are being used to solve a variety of problems in the electronics industry. This work provides the results which have been obtained in the electronics industry. It also presents a survey of numerical methods used in the electronic industry.