The book provides a comprehensive introduction to compact finite
difference methods for solving boundary value ODEs with high
accuracy. The corresponding theory is based on exact difference
schemes (EDS) from which the implementable truncated difference
schemes (TDS) are derived. The TDS are now competitive in terms of
efficiency and accuracy with the well-studied numerical algorithms
for the solution of initial value ODEs. Moreover, various a
posteriori error estimators are presented which can be used in
adaptive algorithms as important building blocks. The new class of
EDS and TDS treated in this book can be considered as further
developments of the results presented in the highly respected books
of the Russian mathematician A. A. Samarskii. It is shown that the
new Samarskii-like techniques open the horizon for the numerical
treatment of more complicated problems. The book contains exercises
and the corresponding solutions enabling the use as a course text
or for self-study. Researchers and students from numerical methods,
engineering and other sciences will find this book provides an
accessible and self-contained introduction to numerical methods for
solving boundary value ODEs.
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