The State of the Art in Numerical Analysis
Author: David A. H. Jacobs
Publisher:
Published: 1977
Total Pages: 1004
ISBN-13:
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Author: David A. H. Jacobs
Publisher:
Published: 1977
Total Pages: 1004
ISBN-13:
DOWNLOAD EBOOKAuthor: Sören Bartels
Publisher: Springer
Published: 2015-01-19
Total Pages: 394
ISBN-13: 3319137972
DOWNLOAD EBOOKThe description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
Author: David F. Griffiths
Publisher: Springer Science & Business Media
Published: 2010-11-11
Total Pages: 274
ISBN-13: 0857291483
DOWNLOAD EBOOKNumerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Author: Larkin Ridgway Scott
Publisher: Princeton University Press
Published: 2011-04-18
Total Pages: 342
ISBN-13: 1400838967
DOWNLOAD EBOOKComputational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin
Author: Carlotta Giannelli
Publisher: Springer Nature
Published: 2019-09-18
Total Pages: 242
ISBN-13: 3030273318
DOWNLOAD EBOOKThis book gathers selected contributions presented at the INdAM Workshop “DREAMS”, held in Rome, Italy on January 22−26, 2018. Addressing cutting-edge research topics and advances in computer aided geometric design and isogeometric analysis, it covers distinguishing curve/surface constructions and spline models, with a special focus on emerging adaptive spline constructions, fundamental spline theory and related algorithms, as well as various aspects of isogeometric methods, e.g. efficient quadrature rules and spectral analysis for isogeometric B-spline discretizations. Applications in finite element and boundary element methods are also discussed. Given its scope, the book will be of interest to both researchers and graduate students working in these areas.
Author: J.M.P.Q. Delgado
Publisher: Springer Science & Business Media
Published: 2012-06-25
Total Pages: 317
ISBN-13: 3642305326
DOWNLOAD EBOOKThe purpose of ‘Numerical Analysis of Heat and Mass Transfer in Porous Media’ is to provide a collection of recent contributions in the field of computational heat and mass transfer in porous media. The main benefit of the book is that it discusses the majority of the topics related to numerical transport phenomenon in engineering (including state-of-the-art and applications) and presents some of the most important theoretical and computational developments in porous media and transport phenomenon domain, providing a self-contained major reference that is appealing to both the scientists, researchers and the engineers. At the same time, these topics encounter of a variety of scientific and engineering disciplines, such as chemical, civil, agricultural, mechanical engineering, etc. The book is divided in several chapters that intend to be a resume of the current state of knowledge for benefit of professional colleagues.
Author:
Publisher:
Published: 1985
Total Pages: 158
ISBN-13:
DOWNLOAD EBOOKAuthor: J. E. Dennis, Jr.
Publisher: SIAM
Published: 1996-12-01
Total Pages: 394
ISBN-13: 9781611971200
DOWNLOAD EBOOKThis book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.
Author: G. M. Phillips
Publisher: Elsevier
Published: 1996-07-05
Total Pages: 461
ISBN-13: 0080519121
DOWNLOAD EBOOKTheory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. - a unique blend of theory and applications - two brand new chapters on eigenvalues and splines - inclusion of formal algorithms - numerous fully worked examples - a large number of problems, many with solutions
Author: Frank Natterer
Publisher: SIAM
Published: 2001-01-01
Total Pages: 226
ISBN-13: 0898716225
DOWNLOAD EBOOKThis book provides readers with a superior understanding of the mathematical principles behind imaging.