This book is about solving partial differential equations (PDEs) . Such equations
are used to model a wide range of phenomena in virtually all fields of science
and technology. In the last decade, the general availability of extremely
powerful computers has shifted the focus in computational mathematics from
simplified model problems to much more sophisticated models resembling intricate
features of real life. This change challenges our knowledge in computer
science and in numerical analysis.
The main objective of the present book is to teach modern, advanced techniques
for numerical PDE solution. The book also introduces several models
arising in fields like finance, medicine, material technology, and geology. In order
to read this book, you must have a basic knowledge of partial differential
equations and numerical methods for solving such equations. Furthermore,
some background in finite element methods is required. You do not need to
know Diffpack, although this programming environment is used in examples
throughout the text. Basically, this book is about models, methods, and how
to implement the methods. For the implementation part it is natural for us
to use Diffpack as the programming environment, because making a PDE
solver in Diffpack requires little amount of programming and because Diffpack
has support for the advanced numerical methods treated in this book .
Most chapters have a part on models and methods, and a part on implementation
and Diffpack programming. The exposition is designed such that
readers can focus only on the first part, if desired. The prerequisites for the
present book (PDEs and numerics) as well as an introduction to Diffpack
programming can be found in "Computational Partial Differential Equations
- Numerical Methods and Diffpack Programming" by H. P. Langtangen.