Numerical Analysis Using R 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” fux 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 demon- strate how numerical methods can be used to tackle very different complex problems. With its focus on practical solutions to real-world problems, this book is useful to students and practitioners in all areas of science and engineering, especially those using R. R Code is available for download from the book’s home page. Graham W. Griffths is a visiting professor in the School of Engineering and Mathematical Sciences, City University London. His primary interests are in numerical methods and climate modeling, on which he has previously pub- lished four books. Griffths was a founder of Special Analysis and Simulation Technology Ltd. and later became 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. www.cambridge.org © in this web service Cambridge University Press Cambridge University Press 978-1-107-11561-3 - Numerical Analysis Using R: Solutions to ODEs and PDEs Graham W. Griffiths Frontmatter More information