Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation) 2009th Edition by David A. Kopriva (PDF)

Description

This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

User’s Reviews

Editorial Reviews: Review From the reviews:“This book focuses on the implementation aspects of spectral methods. … serve as a textbook for graduate students and applied mathematics researchers who seek a practical way to implement spectral algorithms. The presentation is pedagogical, moving from algorithms that are easy to understand to ones that are more complex and involved. … It is a very recommendable book for a graduate course on spectral methods, and covers more practical subjects that are not usually treated in detail in other monographs on spectral methods.”­­­ (Javier de Frutos, Mathematical Reviews, Issue 2010 j) From the Back Cover This book offers a systematic and self-contained approach to solve partial differential equations numerically using single and multidomain spectral methods. It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing potentials, transport, and wave propagation. David Kopriva, a well-known researcher in the field with extensive practical experience, shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries. The book addresses computational and applications scientists, as it emphasizes the practical derivation and implementation of spectral methods over abstract mathematics. It is divided into two parts: First comes a primer on spectral approximation and the basic algorithms, including FFT algorithms, Gauss quadrature algorithms, and how to approximate derivatives. The second part shows how to use those algorithms to solve steady and time dependent PDEs in one and two space dimensions. Exercises and questions at the end of each chapter encourage the reader to experiment with the algorithms. About the Author David Kopriva is Professor of Mathematics at the Florida State University, where he has taught since 1985. He is an expert in the development, implementation and application of high order spectral multi-domain methods for time dependent problems. In 1986 he developed the first multi-domain spectral method for hyperbolic systems, which was applied to the Euler equations of gas dynamics. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐As somebody who is partially self-taught in Spectral Methods but has also had the luxury to being taught by some of the leading figures in the field, I will insist that I love this book. It’s a very solid introduction, highly geared toward the vocabulary of physicists and engineers (i.e. not loss in endless proofs) with a very helpful bend on actual implementation. The 4 first chapters include everything you need to know on different spectral discretizations in one dimension. More complex topics are illustrated in subsequent chapters with the various coding examples being incredibly useful. I also like the forays into numerical linear algebra, a field that is inevitably intertwined with higher order methods.It’s obvious that Prof. Kopriva cares about the reader learning the material on these highly powerful but highly complex techniques. I have actually used this book in teaching an advanced Master’s level course on the topic and it has been very well received by the students. I enthusiastically recommend this book to anybody who wants to learn more on these methods and I really wish it was around when I started exploring them back in 2001.

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Free Download Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation) 2009th Edition in PDF format
Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation) 2009th Edition PDF Free Download
Download Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation) 2009th Edition 2009 PDF Free
Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation) 2009th Edition 2009 PDF Free Download
Download Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers (Scientific Computation) 2009th Edition PDF
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