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.Read more
- Practical solutions to ODEs and PDEs using computer code
- Overviews of 'high resolution' schemes and meshless methods
- Case studies illustrating the use of numerical analysis in a real-world setting
Reviews & endorsements
'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, PennsylvaniaSee more reviews
'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
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- Date Published: July 2016
- format: Hardback
- isbn: 9781107115613
- dimensions: 260 x 183 x 37 mm
- weight: 1.3kg
- contains: 182 b/w illus. 15 colour illus.
- availability: Temporarily unavailable - available from July 2017
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.
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