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"Aimed at students and researchers entering the field, this pedagogical introduction to numerical relativity will also interest scientists seeking a broad survey of its challenges and achievements. --Assuming only a basic knowledge of classical general relativity, this textbook develops the mathematical formalism from first principles, then highlights some of the pioneering simulations involving black holes and neutron stars, gravitational collapse and gravitational waves. --Applications include calculations of coalescing binary black holes and binary neutron stars, rotating stars, colliding star clusters, gravitational and magnetorotational collapse, critical phenomena, the generation of gravitational waves, and many more. --"...an excellent introduction...covering both mathematical aspects and numerical techniques... The authors are world leaders in numerical relativity...This book will soon become the standard advanced text for younger researchers entering the field and will also serve as the authoritative reference for senior researchers..." Abhay Ashtekhar, Director, Institute for Gravitation and the Cosmos, The Pennsylvania State University --"Numerical relativity has come of age...Two leading experts give a lucid as well as richly detailed account building a bridge from the basics to current research-highly recommended." Bernd Brugmann, Friedrich-Schiller-Universitot --"...what a book this is!...a genuine learning manual...exceedingly well written...covers virtually all aspects of numerical relativity...replete with beautiful and helpful diagrams...a useful reference to the researcher and a source of enlightenment to many a student...." Eric Poisson, University of Guelph --"Baumgarte and Shapiro are established leaders in this subject. Their book is a timely contribution to the literature, and the ideal primer for researchers newly attracted to the burgeoning field of computational relativity." Martin Rees, Astronomer Royal and Master of Trinity College, Cambridge --Book Jacket."

"A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing -- the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering."

"This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well.The author bridges theory and practice by developing algorithms, concepts, and analysis from basic principles while discussing efficiency and performance issues and demonstrating methods through examples and case studies from numerous application areas."

"Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises."