Numerical Analysis Using R: Solutions to ODEs and PDEs

by Graham W. Griffiths

Overview

This book presents the latest numerical solutions to initial value problems and boundary value problems described by ODEs and PDEs. The author offers practical methods that can be adapted to solve wide ranges of problems and illustrates them in the increasingly popular open source computer language R, allowing integration with more statistically based methods. The book begins with standard techniques, followed by an overview of 'high resolution' flux limiters and WENO to solve problems with solutions exhibiting high gradient phenomena. Meshless methods using radial basis functions are then discussed in the context of scattered data interpolation and the solution of PDEs on irregular grids. Three detailed case studies demonstrate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book will be useful to students and practitioners in all areas of science and engineering, especially those using R.

Product Details

ISBN-13:	9781316653104
Publisher:	Cambridge University Press
Publication date:	04/26/2016
Sold by:	Barnes & Noble
Format:	eBook
File size:	223 MB
Note:	This product may take a few minutes to download.

About the Author

Graham W. Griffiths is a visiting professor in the School of Engineering and Mathematical Sciences, City University, London. His primary interests are in numerical methods and climate modelling, on which he has previously published four books. Griffiths was a founder of Special Analysis and Simulation Technology Ltd, and later vice president of operations and technology with AspenTech. He is a Chartered Engineer and a Fellow of the Institute of Measurement and Control, and was granted Freedom of the City of London in 1995.

Table of Contents

1. ODE integration methods; 2. Stability analysis of ODE integrators; 3. Numerical solution of PDEs; 4. PDE stability analysis; 5. Dissipation and dispersion; 6. High resolution schemes; 7. Meshless methods; 8. Conservation laws; 9. Case study: analysis of golf ball flight; 10. Case study: Taylor–Sedov blast wave; 11. Case study: the carbon cycle.

Editorial Reviews

"Graham W. Griffiths has produced an outstanding contribution to scientific computation, specifically, the numerical solution of a series of real-world ODE/PDE models. The format of each chapter, i.e. a detailed discussion of the origin of each model, a listing of the commented R routines with background for the numerical algorithms, and an analysis of the computed solutions, permits the reader to immediately understand and execute each model."
W. E. Schiesser, Lehigh University, Pennsylvania

"This book is truly a compendium of numerical methods. The R code listings enhance the exposition greatly. Written in a practical manner, it culminates in case-study chapters where the reader is beautifully led through fascinating applied topics. It is an enjoyable read for anyone interested in modern numerical analysis."
Łukasz Płociniczak, Wrocław University of Technology

'Numerical Analysis Using R is a very interesting text on the theory and practical implementation of numerical methods for approximating solutions to differential equations. The book contains a wealth of information presented in such a way as to be accessible to a wide audience of engineers, mathematicians and other scientists. This book manages to be a unique contribution to the collection of numerical methods texts …' Jason M. Graham, MAA Reviews

From the Publisher