General Linear Methods for Ordinary Differential Equations (PDF)

Learn to develop numerical methods for ordinary differential
equations

General Linear Methods for Ordinary Differential Equations fills
a gap in the existing literature by presenting a comprehensive and
up-to-date collection of recent advances and developments in the
field. This book provides modern coverage of the theory,
construction, and implementation of both classical and modern
general linear methods for solving ordinary differential equations
as they apply to a variety of related areas, including mathematics,
applied science, and engineering.

The author provides the theoretical foundation for understanding
basic concepts and presents a short introduction to ordinary
differential equations that encompasses the related concepts of
existence and uniqueness theory, stability theory, and stiff
differential equations and systems. In addition, a thorough
presentation of general linear methods explores relevant subtopics
such as pre-consistency, consistency, stage-consistency, zero
stability, convergence, order- and stage-order conditions, local
discretization error, and linear stability theory. Subsequent
chapters feature coverage of:

* Differential equations and systems

* Introduction to general linear methods (GLMs)

* Diagonally implicit multistage integration methods (DIMSIMs)

* Implementation of DIMSIMs

* Two-step Runge-Kutta (TSRK) methods

* Implementation of TSRK methods

* GLMs with inherent Runge-Kutta stability (IRKS)

* Implementation of GLMs with IRKS

General Linear Methods for Ordinary Differential Equations is an
excellent book for courses on numerical ordinary differential
equations at the upper-undergraduate and graduate levels. It is
also a useful reference for academic and research professionals in
the fields of computational and applied mathematics, computational
physics, civil and chemical engineering, chemistry, and the life
sciences.