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.
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