This comprehensive primer on compact finite difference methods for solving boundary value ODEs with high accuracy includes coverage of various a posteriori error estimators which are ideal for use in adaptive algorithms as important building blocks.

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...

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). It includes a range of problems and examples, ranging from the elementary to the challenging.